How do you graph #1/(2x)#?

Answer 1

Please see the explanation.

Given:

#color(red)(y = f(x) = 1/(2x)#

To graph this rational function, we can create a table of values.

The values of #color(red)(x# can be chosen as suggested below, both positive and negative.

Using #color(red)(y = 1/(2x)# we can find the corresponding values for #color(red)(y#.

An image of the graph of the rational function #color(red)(y = 1/(2x)# is below:

For rational functions the Vertical Asymptotes are the undefined points known as the Zeros of the denominator of the simplified rational functions.

In the graph above, we observe that the Vertical Asymptote is #x =0.#

Horizontal Asymptote:

The highest degree of the numerator = 0.

The highest degree of the denominator = 1.

Since the denominator’s degree > numerator's degree, the horizontal asymptote is the x-axis, #y = 0.#

For the sake of clarity and better comprehension, the spreadsheet table below contains values for the parent function #color(red)(y = f(x) = 1/(x)# also.

One can compare both the tables to understand the behavior of the rational function #color(red)(y = 1/(2x)#

Using the table above, we can plot the points as an ordered pair #(x,y)# and create a graph as shown below:

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Answer 2

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1.To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  1. Identify the verticalTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  2. Identify the vertical asymptTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  3. Identify the domainTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  4. Identify the vertical asymptoteTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  5. Identify the domain ofTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  6. Identify the vertical asymptote: To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  7. Identify the domain of theTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  8. Identify the vertical asymptote: To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  9. Identify the domain of the functionTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  10. Identify the vertical asymptote: -To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  11. Identify the domain of the function,To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  12. Identify the vertical asymptote:

    • TheTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  13. Identify the domain of the function, whichTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  14. Identify the vertical asymptote:

    • The functionTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  15. Identify the domain of the function, which isTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  16. Identify the vertical asymptote:

    • The function (To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  17. Identify the domain of the function, which is allTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  18. Identify the vertical asymptote:

    • The function ( fTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  19. Identify the domain of the function, which is all realTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  20. Identify the vertical asymptote:

    • The function ( f(xTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  21. Identify the domain of the function, which is all real numbersTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  22. Identify the vertical asymptote:

    • The function ( f(x)To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  23. Identify the domain of the function, which is all real numbers exceptTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  24. Identify the vertical asymptote:

    • The function ( f(x) \To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  25. Identify the domain of the function, which is all real numbers except (To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  26. Identify the vertical asymptote:

    • The function ( f(x) )To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  27. Identify the domain of the function, which is all real numbers except ( xTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  28. Identify the vertical asymptote:

    • The function ( f(x) ) hasTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  29. Identify the domain of the function, which is all real numbers except ( x = To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  30. Identify the vertical asymptote:

    • The function ( f(x) ) has a verticalTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  31. Identify the domain of the function, which is all real numbers except ( x = 0To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  32. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  33. Identify the domain of the function, which is all real numbers except ( x = 0 \To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  34. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptoteTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  35. Identify the domain of the function, which is all real numbers except ( x = 0 )To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  36. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote atTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  37. Identify the domain of the function, which is all real numbers except ( x = 0 ) sinceTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  38. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at (To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  39. Identify the domain of the function, which is all real numbers except ( x = 0 ) since divisionTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  40. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( xTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  41. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division byTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  42. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x =To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  43. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zeroTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  44. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  45. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero isTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  46. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  47. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefinedTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  48. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 \To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  49. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined. To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  50. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 )To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  51. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined. 2To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  52. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) becauseTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  53. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined. 2.To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  54. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because theTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  55. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  56. ChooseTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  57. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominatorTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  58. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  59. Choose severalTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  60. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannotTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  61. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  62. Choose several valuesTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  63. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equalTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  64. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  65. Choose several values ofTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  66. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zeroTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  67. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  68. Choose several values of (To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  69. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.

To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  1. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  2. Choose several values of ( xTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  3. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.

2To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  1. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  2. Choose several values of ( x \To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  3. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.

2.To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  1. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  2. Choose several values of ( x )To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  3. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  4. DetermineTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  5. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  6. Choose several values of ( x ) toTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  7. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  8. Determine theTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  9. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  10. Choose several values of ( x ) to evaluateTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  11. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  12. Determine the behaviorTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  13. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  14. Choose several values of ( x ) to evaluate theTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  15. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  16. Determine the behavior asTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  17. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  18. Choose several values of ( x ) to evaluate the function.To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  19. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  20. Determine the behavior as ( xTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  21. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  22. Choose several values of ( x ) to evaluate the function. YouTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  23. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  24. Determine the behavior as ( x \To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  25. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  26. Choose several values of ( x ) to evaluate the function. You mayTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  27. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  28. Determine the behavior as ( x )To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  29. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  30. Choose several values of ( x ) to evaluate the function. You may pickTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  31. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  32. Determine the behavior as ( x ) approachesTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  33. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  34. Choose several values of ( x ) to evaluate the function. You may pick valuesTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  35. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  36. Determine the behavior as ( x ) approaches positiveTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  37. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  38. Choose several values of ( x ) to evaluate the function. You may pick values bothTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  39. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  40. Determine the behavior as ( x ) approaches positive andTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  41. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  42. Choose several values of ( x ) to evaluate the function. You may pick values both greaterTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  43. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  44. Determine the behavior as ( x ) approaches positive and negativeTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  45. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  46. Choose several values of ( x ) to evaluate the function. You may pick values both greater and lessTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  47. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  48. Determine the behavior as ( x ) approaches positive and negative infinity: To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  49. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  50. Choose several values of ( x ) to evaluate the function. You may pick values both greater and less thanTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  51. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  52. Determine the behavior as ( x ) approaches positive and negative infinity:

    • As (To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  53. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  54. Choose several values of ( x ) to evaluate the function. You may pick values both greater and less than zero to seeTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  55. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  56. Determine the behavior as ( x ) approaches positive and negative infinity:

    • As ( xTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  57. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  58. Choose several values of ( x ) to evaluate the function. You may pick values both greater and less than zero to see the behaviorTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  59. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  60. Determine the behavior as ( x ) approaches positive and negative infinity:

    • As ( x \To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  61. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  62. Choose several values of ( x ) to evaluate the function. You may pick values both greater and less than zero to see the behavior onTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  63. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  64. Determine the behavior as ( x ) approaches positive and negative infinity:

    • As ( x )To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  65. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  66. Choose several values of ( x ) to evaluate the function. You may pick values both greater and less than zero to see the behavior on bothTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  67. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  68. Determine the behavior as ( x ) approaches positive and negative infinity:

    • As ( x ) approachesTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  69. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  70. Choose several values of ( x ) to evaluate the function. You may pick values both greater and less than zero to see the behavior on both sidesTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  71. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  72. Determine the behavior as ( x ) approaches positive and negative infinity:

    • As ( x ) approaches positiveTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  73. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  74. Choose several values of ( x ) to evaluate the function. You may pick values both greater and less than zero to see the behavior on both sides. 3To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  75. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  76. Determine the behavior as ( x ) approaches positive and negative infinity:

    • As ( x ) approaches positive infinityTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  77. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  78. Choose several values of ( x ) to evaluate the function. You may pick values both greater and less than zero to see the behavior on both sides. 3.To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  79. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  80. Determine the behavior as ( x ) approaches positive and negative infinity:

    • As ( x ) approaches positive infinity,To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  81. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  82. Choose several values of ( x ) to evaluate the function. You may pick values both greater and less than zero to see the behavior on both sides.

  83. CalculateTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  84. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  85. Determine the behavior as ( x ) approaches positive and negative infinity:

    • As ( x ) approaches positive infinity, ( fTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  86. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  87. Choose several values of ( x ) to evaluate the function. You may pick values both greater and less than zero to see the behavior on both sides.

  88. Calculate theTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  89. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  90. Determine the behavior as ( x ) approaches positive and negative infinity:

    • As ( x ) approaches positive infinity, ( f(xTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  91. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  92. Choose several values of ( x ) to evaluate the function. You may pick values both greater and less than zero to see the behavior on both sides.

  93. Calculate the correspondingTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  94. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  95. Determine the behavior as ( x ) approaches positive and negative infinity:

    • As ( x ) approaches positive infinity, ( f(x)To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  96. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  97. Choose several values of ( x ) to evaluate the function. You may pick values both greater and less than zero to see the behavior on both sides.

  98. Calculate the corresponding valuesTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  99. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  100. Determine the behavior as ( x ) approaches positive and negative infinity:

    • As ( x ) approaches positive infinity, ( f(x) \To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  101. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  102. Choose several values of ( x ) to evaluate the function. You may pick values both greater and less than zero to see the behavior on both sides.

  103. Calculate the corresponding values ofTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  104. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  105. Determine the behavior as ( x ) approaches positive and negative infinity:

    • As ( x ) approaches positive infinity, ( f(x) )To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  106. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  107. Choose several values of ( x ) to evaluate the function. You may pick values both greater and less than zero to see the behavior on both sides.

  108. Calculate the corresponding values of (To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  109. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  110. Determine the behavior as ( x ) approaches positive and negative infinity:

    • As ( x ) approaches positive infinity, ( f(x) ) approachesTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  111. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  112. Choose several values of ( x ) to evaluate the function. You may pick values both greater and less than zero to see the behavior on both sides.

  113. Calculate the corresponding values of ( fTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  114. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  115. Determine the behavior as ( x ) approaches positive and negative infinity:

    • As ( x ) approaches positive infinity, ( f(x) ) approaches zeroTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  116. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  117. Choose several values of ( x ) to evaluate the function. You may pick values both greater and less than zero to see the behavior on both sides.

  118. Calculate the corresponding values of ( f(xTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  119. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  120. Determine the behavior as ( x ) approaches positive and negative infinity:

    • As ( x ) approaches positive infinity, ( f(x) ) approaches zero. To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  121. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  122. Choose several values of ( x ) to evaluate the function. You may pick values both greater and less than zero to see the behavior on both sides.

  123. Calculate the corresponding values of ( f(x)To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  124. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  125. Determine the behavior as ( x ) approaches positive and negative infinity:

    • As ( x ) approaches positive infinity, ( f(x) ) approaches zero. To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  126. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  127. Choose several values of ( x ) to evaluate the function. You may pick values both greater and less than zero to see the behavior on both sides.

  128. Calculate the corresponding values of ( f(x) \To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  129. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  130. Determine the behavior as ( x ) approaches positive and negative infinity:

    • As ( x ) approaches positive infinity, ( f(x) ) approaches zero. -To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  131. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  132. Choose several values of ( x ) to evaluate the function. You may pick values both greater and less than zero to see the behavior on both sides.

  133. Calculate the corresponding values of ( f(x) )To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  134. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  135. Determine the behavior as ( x ) approaches positive and negative infinity:

    • As ( x ) approaches positive infinity, ( f(x) ) approaches zero.
    • AsTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  136. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  137. Choose several values of ( x ) to evaluate the function. You may pick values both greater and less than zero to see the behavior on both sides.

  138. Calculate the corresponding values of ( f(x) ) usingTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  139. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  140. Determine the behavior as ( x ) approaches positive and negative infinity:

    • As ( x ) approaches positive infinity, ( f(x) ) approaches zero.
    • As (To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  141. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  142. Choose several values of ( x ) to evaluate the function. You may pick values both greater and less than zero to see the behavior on both sides.

  143. Calculate the corresponding values of ( f(x) ) using the functionTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  144. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  145. Determine the behavior as ( x ) approaches positive and negative infinity:

    • As ( x ) approaches positive infinity, ( f(x) ) approaches zero.
    • As ( x \To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  146. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  147. Choose several values of ( x ) to evaluate the function. You may pick values both greater and less than zero to see the behavior on both sides.

  148. Calculate the corresponding values of ( f(x) ) using the function (To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  149. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  150. Determine the behavior as ( x ) approaches positive and negative infinity:

    • As ( x ) approaches positive infinity, ( f(x) ) approaches zero.
    • As ( x )To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  151. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  152. Choose several values of ( x ) to evaluate the function. You may pick values both greater and less than zero to see the behavior on both sides.

  153. Calculate the corresponding values of ( f(x) ) using the function ( fTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  154. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  155. Determine the behavior as ( x ) approaches positive and negative infinity:

    • As ( x ) approaches positive infinity, ( f(x) ) approaches zero.
    • As ( x ) approachesTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  156. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  157. Choose several values of ( x ) to evaluate the function. You may pick values both greater and less than zero to see the behavior on both sides.

  158. Calculate the corresponding values of ( f(x) ) using the function ( f(x)To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  159. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  160. Determine the behavior as ( x ) approaches positive and negative infinity:

    • As ( x ) approaches positive infinity, ( f(x) ) approaches zero.
    • As ( x ) approaches negative infinityTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  161. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  162. Choose several values of ( x ) to evaluate the function. You may pick values both greater and less than zero to see the behavior on both sides.

  163. Calculate the corresponding values of ( f(x) ) using the function ( f(x) =To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  164. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  165. Determine the behavior as ( x ) approaches positive and negative infinity:

    • As ( x ) approaches positive infinity, ( f(x) ) approaches zero.
    • As ( x ) approaches negative infinity,To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  166. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  167. Choose several values of ( x ) to evaluate the function. You may pick values both greater and less than zero to see the behavior on both sides.

  168. Calculate the corresponding values of ( f(x) ) using the function ( f(x) = \fracTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  169. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  170. Determine the behavior as ( x ) approaches positive and negative infinity:

    • As ( x ) approaches positive infinity, ( f(x) ) approaches zero.
    • As ( x ) approaches negative infinity, ( fTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  171. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  172. Choose several values of ( x ) to evaluate the function. You may pick values both greater and less than zero to see the behavior on both sides.

  173. Calculate the corresponding values of ( f(x) ) using the function ( f(x) = \frac{To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  174. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  175. Determine the behavior as ( x ) approaches positive and negative infinity:

    • As ( x ) approaches positive infinity, ( f(x) ) approaches zero.
    • As ( x ) approaches negative infinity, ( f(xTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  176. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  177. Choose several values of ( x ) to evaluate the function. You may pick values both greater and less than zero to see the behavior on both sides.

  178. Calculate the corresponding values of ( f(x) ) using the function ( f(x) = \frac{1To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  179. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  180. Determine the behavior as ( x ) approaches positive and negative infinity:

    • As ( x ) approaches positive infinity, ( f(x) ) approaches zero.
    • As ( x ) approaches negative infinity, ( f(x)To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  181. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  182. Choose several values of ( x ) to evaluate the function. You may pick values both greater and less than zero to see the behavior on both sides.

  183. Calculate the corresponding values of ( f(x) ) using the function ( f(x) = \frac{1}{2To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  184. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  185. Determine the behavior as ( x ) approaches positive and negative infinity:

    • As ( x ) approaches positive infinity, ( f(x) ) approaches zero.
    • As ( x ) approaches negative infinity, ( f(x) \To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  186. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  187. Choose several values of ( x ) to evaluate the function. You may pick values both greater and less than zero to see the behavior on both sides.

  188. Calculate the corresponding values of ( f(x) ) using the function ( f(x) = \frac{1}{2xTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  189. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  190. Determine the behavior as ( x ) approaches positive and negative infinity:

    • As ( x ) approaches positive infinity, ( f(x) ) approaches zero.
    • As ( x ) approaches negative infinity, ( f(x) )To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  191. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  192. Choose several values of ( x ) to evaluate the function. You may pick values both greater and less than zero to see the behavior on both sides.

  193. Calculate the corresponding values of ( f(x) ) using the function ( f(x) = \frac{1}{2x}To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  194. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  195. Determine the behavior as ( x ) approaches positive and negative infinity:

    • As ( x ) approaches positive infinity, ( f(x) ) approaches zero.
    • As ( x ) approaches negative infinity, ( f(x) ) approachesTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  196. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  197. Choose several values of ( x ) to evaluate the function. You may pick values both greater and less than zero to see the behavior on both sides.

  198. Calculate the corresponding values of ( f(x) ) using the function ( f(x) = \frac{1}{2x} \To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  199. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  200. Determine the behavior as ( x ) approaches positive and negative infinity:

    • As ( x ) approaches positive infinity, ( f(x) ) approaches zero.
    • As ( x ) approaches negative infinity, ( f(x) ) approaches zeroTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  201. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  202. Choose several values of ( x ) to evaluate the function. You may pick values both greater and less than zero to see the behavior on both sides.

  203. Calculate the corresponding values of ( f(x) ) using the function ( f(x) = \frac{1}{2x} ). To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  204. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  205. Determine the behavior as ( x ) approaches positive and negative infinity:

    • As ( x ) approaches positive infinity, ( f(x) ) approaches zero.
    • As ( x ) approaches negative infinity, ( f(x) ) approaches zero.

To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  1. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  2. Choose several values of ( x ) to evaluate the function. You may pick values both greater and less than zero to see the behavior on both sides.

  3. Calculate the corresponding values of ( f(x) ) using the function ( f(x) = \frac{1}{2x} ). 4To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  4. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  5. Determine the behavior as ( x ) approaches positive and negative infinity:

    • As ( x ) approaches positive infinity, ( f(x) ) approaches zero.
    • As ( x ) approaches negative infinity, ( f(x) ) approaches zero.

3To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  1. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  2. Choose several values of ( x ) to evaluate the function. You may pick values both greater and less than zero to see the behavior on both sides.

  3. Calculate the corresponding values of ( f(x) ) using the function ( f(x) = \frac{1}{2x} ). 4.To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  4. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  5. Determine the behavior as ( x ) approaches positive and negative infinity:

    • As ( x ) approaches positive infinity, ( f(x) ) approaches zero.
    • As ( x ) approaches negative infinity, ( f(x) ) approaches zero.
  6. PlotTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  7. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  8. Choose several values of ( x ) to evaluate the function. You may pick values both greater and less than zero to see the behavior on both sides.

  9. Calculate the corresponding values of ( f(x) ) using the function ( f(x) = \frac{1}{2x} ).

  10. PlotTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  11. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  12. Determine the behavior as ( x ) approaches positive and negative infinity:

    • As ( x ) approaches positive infinity, ( f(x) ) approaches zero.
    • As ( x ) approaches negative infinity, ( f(x) ) approaches zero.
  13. Plot additionalTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  14. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  15. Choose several values of ( x ) to evaluate the function. You may pick values both greater and less than zero to see the behavior on both sides.

  16. Calculate the corresponding values of ( f(x) ) using the function ( f(x) = \frac{1}{2x} ).

  17. Plot theTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  18. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  19. Determine the behavior as ( x ) approaches positive and negative infinity:

    • As ( x ) approaches positive infinity, ( f(x) ) approaches zero.
    • As ( x ) approaches negative infinity, ( f(x) ) approaches zero.
  20. Plot additional pointsTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  21. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  22. Choose several values of ( x ) to evaluate the function. You may pick values both greater and less than zero to see the behavior on both sides.

  23. Calculate the corresponding values of ( f(x) ) using the function ( f(x) = \frac{1}{2x} ).

  24. Plot the pointsTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  25. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  26. Determine the behavior as ( x ) approaches positive and negative infinity:

    • As ( x ) approaches positive infinity, ( f(x) ) approaches zero.
    • As ( x ) approaches negative infinity, ( f(x) ) approaches zero.
  27. Plot additional points ifTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  28. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  29. Choose several values of ( x ) to evaluate the function. You may pick values both greater and less than zero to see the behavior on both sides.

  30. Calculate the corresponding values of ( f(x) ) using the function ( f(x) = \frac{1}{2x} ).

  31. Plot the points (To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  32. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  33. Determine the behavior as ( x ) approaches positive and negative infinity:

    • As ( x ) approaches positive infinity, ( f(x) ) approaches zero.
    • As ( x ) approaches negative infinity, ( f(x) ) approaches zero.
  34. Plot additional points if necessaryTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  35. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  36. Choose several values of ( x ) to evaluate the function. You may pick values both greater and less than zero to see the behavior on both sides.

  37. Calculate the corresponding values of ( f(x) ) using the function ( f(x) = \frac{1}{2x} ).

  38. Plot the points ( (To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  39. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  40. Determine the behavior as ( x ) approaches positive and negative infinity:

    • As ( x ) approaches positive infinity, ( f(x) ) approaches zero.
    • As ( x ) approaches negative infinity, ( f(x) ) approaches zero.
  41. Plot additional points if necessary: To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  42. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  43. Choose several values of ( x ) to evaluate the function. You may pick values both greater and less than zero to see the behavior on both sides.

  44. Calculate the corresponding values of ( f(x) ) using the function ( f(x) = \frac{1}{2x} ).

  45. Plot the points ( (xTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  46. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  47. Determine the behavior as ( x ) approaches positive and negative infinity:

    • As ( x ) approaches positive infinity, ( f(x) ) approaches zero.
    • As ( x ) approaches negative infinity, ( f(x) ) approaches zero.
  48. Plot additional points if necessary: To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  49. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  50. Choose several values of ( x ) to evaluate the function. You may pick values both greater and less than zero to see the behavior on both sides.

  51. Calculate the corresponding values of ( f(x) ) using the function ( f(x) = \frac{1}{2x} ).

  52. Plot the points ( (x,To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  53. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  54. Determine the behavior as ( x ) approaches positive and negative infinity:

    • As ( x ) approaches positive infinity, ( f(x) ) approaches zero.
    • As ( x ) approaches negative infinity, ( f(x) ) approaches zero.
  55. Plot additional points if necessary: -To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  56. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  57. Choose several values of ( x ) to evaluate the function. You may pick values both greater and less than zero to see the behavior on both sides.

  58. Calculate the corresponding values of ( f(x) ) using the function ( f(x) = \frac{1}{2x} ).

  59. Plot the points ( (x, fTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  60. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  61. Determine the behavior as ( x ) approaches positive and negative infinity:

    • As ( x ) approaches positive infinity, ( f(x) ) approaches zero.
    • As ( x ) approaches negative infinity, ( f(x) ) approaches zero.
  62. Plot additional points if necessary:

    • ChooseTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  63. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  64. Choose several values of ( x ) to evaluate the function. You may pick values both greater and less than zero to see the behavior on both sides.

  65. Calculate the corresponding values of ( f(x) ) using the function ( f(x) = \frac{1}{2x} ).

  66. Plot the points ( (x, f(xTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  67. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  68. Determine the behavior as ( x ) approaches positive and negative infinity:

    • As ( x ) approaches positive infinity, ( f(x) ) approaches zero.
    • As ( x ) approaches negative infinity, ( f(x) ) approaches zero.
  69. Plot additional points if necessary:

    • Choose someTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  70. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  71. Choose several values of ( x ) to evaluate the function. You may pick values both greater and less than zero to see the behavior on both sides.

  72. Calculate the corresponding values of ( f(x) ) using the function ( f(x) = \frac{1}{2x} ).

  73. Plot the points ( (x, f(x)) \To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  74. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  75. Determine the behavior as ( x ) approaches positive and negative infinity:

    • As ( x ) approaches positive infinity, ( f(x) ) approaches zero.
    • As ( x ) approaches negative infinity, ( f(x) ) approaches zero.
  76. Plot additional points if necessary:

    • Choose some values forTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  77. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  78. Choose several values of ( x ) to evaluate the function. You may pick values both greater and less than zero to see the behavior on both sides.

  79. Calculate the corresponding values of ( f(x) ) using the function ( f(x) = \frac{1}{2x} ).

  80. Plot the points ( (x, f(x)) )To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  81. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  82. Determine the behavior as ( x ) approaches positive and negative infinity:

    • As ( x ) approaches positive infinity, ( f(x) ) approaches zero.
    • As ( x ) approaches negative infinity, ( f(x) ) approaches zero.
  83. Plot additional points if necessary:

    • Choose some values for (To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  84. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  85. Choose several values of ( x ) to evaluate the function. You may pick values both greater and less than zero to see the behavior on both sides.

  86. Calculate the corresponding values of ( f(x) ) using the function ( f(x) = \frac{1}{2x} ).

  87. Plot the points ( (x, f(x)) ) onTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  88. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  89. Determine the behavior as ( x ) approaches positive and negative infinity:

    • As ( x ) approaches positive infinity, ( f(x) ) approaches zero.
    • As ( x ) approaches negative infinity, ( f(x) ) approaches zero.
  90. Plot additional points if necessary:

    • Choose some values for ( xTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  91. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  92. Choose several values of ( x ) to evaluate the function. You may pick values both greater and less than zero to see the behavior on both sides.

  93. Calculate the corresponding values of ( f(x) ) using the function ( f(x) = \frac{1}{2x} ).

  94. Plot the points ( (x, f(x)) ) on theTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  95. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  96. Determine the behavior as ( x ) approaches positive and negative infinity:

    • As ( x ) approaches positive infinity, ( f(x) ) approaches zero.
    • As ( x ) approaches negative infinity, ( f(x) ) approaches zero.
  97. Plot additional points if necessary:

    • Choose some values for ( x \To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  98. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  99. Choose several values of ( x ) to evaluate the function. You may pick values both greater and less than zero to see the behavior on both sides.

  100. Calculate the corresponding values of ( f(x) ) using the function ( f(x) = \frac{1}{2x} ).

  101. Plot the points ( (x, f(x)) ) on the coordinateTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  102. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  103. Determine the behavior as ( x ) approaches positive and negative infinity:

    • As ( x ) approaches positive infinity, ( f(x) ) approaches zero.
    • As ( x ) approaches negative infinity, ( f(x) ) approaches zero.
  104. Plot additional points if necessary:

    • Choose some values for ( x )To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  105. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  106. Choose several values of ( x ) to evaluate the function. You may pick values both greater and less than zero to see the behavior on both sides.

  107. Calculate the corresponding values of ( f(x) ) using the function ( f(x) = \frac{1}{2x} ).

  108. Plot the points ( (x, f(x)) ) on the coordinate planeTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  109. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  110. Determine the behavior as ( x ) approaches positive and negative infinity:

    • As ( x ) approaches positive infinity, ( f(x) ) approaches zero.
    • As ( x ) approaches negative infinity, ( f(x) ) approaches zero.
  111. Plot additional points if necessary:

    • Choose some values for ( x ) andTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  112. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  113. Choose several values of ( x ) to evaluate the function. You may pick values both greater and less than zero to see the behavior on both sides.

  114. Calculate the corresponding values of ( f(x) ) using the function ( f(x) = \frac{1}{2x} ).

  115. Plot the points ( (x, f(x)) ) on the coordinate plane. To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  116. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  117. Determine the behavior as ( x ) approaches positive and negative infinity:

    • As ( x ) approaches positive infinity, ( f(x) ) approaches zero.
    • As ( x ) approaches negative infinity, ( f(x) ) approaches zero.
  118. Plot additional points if necessary:

    • Choose some values for ( x ) and findTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  119. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  120. Choose several values of ( x ) to evaluate the function. You may pick values both greater and less than zero to see the behavior on both sides.

  121. Calculate the corresponding values of ( f(x) ) using the function ( f(x) = \frac{1}{2x} ).

  122. Plot the points ( (x, f(x)) ) on the coordinate plane. 5To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  123. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  124. Determine the behavior as ( x ) approaches positive and negative infinity:

    • As ( x ) approaches positive infinity, ( f(x) ) approaches zero.
    • As ( x ) approaches negative infinity, ( f(x) ) approaches zero.
  125. Plot additional points if necessary:

    • Choose some values for ( x ) and find theTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  126. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  127. Choose several values of ( x ) to evaluate the function. You may pick values both greater and less than zero to see the behavior on both sides.

  128. Calculate the corresponding values of ( f(x) ) using the function ( f(x) = \frac{1}{2x} ).

  129. Plot the points ( (x, f(x)) ) on the coordinate plane. 5.To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  130. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  131. Determine the behavior as ( x ) approaches positive and negative infinity:

    • As ( x ) approaches positive infinity, ( f(x) ) approaches zero.
    • As ( x ) approaches negative infinity, ( f(x) ) approaches zero.
  132. Plot additional points if necessary:

    • Choose some values for ( x ) and find the correspondingTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  133. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  134. Choose several values of ( x ) to evaluate the function. You may pick values both greater and less than zero to see the behavior on both sides.

  135. Calculate the corresponding values of ( f(x) ) using the function ( f(x) = \frac{1}{2x} ).

  136. Plot the points ( (x, f(x)) ) on the coordinate plane.

  137. ConnectTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  138. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  139. Determine the behavior as ( x ) approaches positive and negative infinity:

    • As ( x ) approaches positive infinity, ( f(x) ) approaches zero.
    • As ( x ) approaches negative infinity, ( f(x) ) approaches zero.
  140. Plot additional points if necessary:

    • Choose some values for ( x ) and find the corresponding (To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  141. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  142. Choose several values of ( x ) to evaluate the function. You may pick values both greater and less than zero to see the behavior on both sides.

  143. Calculate the corresponding values of ( f(x) ) using the function ( f(x) = \frac{1}{2x} ).

  144. Plot the points ( (x, f(x)) ) on the coordinate plane.

  145. Connect theTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  146. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  147. Determine the behavior as ( x ) approaches positive and negative infinity:

    • As ( x ) approaches positive infinity, ( f(x) ) approaches zero.
    • As ( x ) approaches negative infinity, ( f(x) ) approaches zero.
  148. Plot additional points if necessary:

    • Choose some values for ( x ) and find the corresponding ( yTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  149. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  150. Choose several values of ( x ) to evaluate the function. You may pick values both greater and less than zero to see the behavior on both sides.

  151. Calculate the corresponding values of ( f(x) ) using the function ( f(x) = \frac{1}{2x} ).

  152. Plot the points ( (x, f(x)) ) on the coordinate plane.

  153. Connect the pointsTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  154. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  155. Determine the behavior as ( x ) approaches positive and negative infinity:

    • As ( x ) approaches positive infinity, ( f(x) ) approaches zero.
    • As ( x ) approaches negative infinity, ( f(x) ) approaches zero.
  156. Plot additional points if necessary:

    • Choose some values for ( x ) and find the corresponding ( y \To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  157. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  158. Choose several values of ( x ) to evaluate the function. You may pick values both greater and less than zero to see the behavior on both sides.

  159. Calculate the corresponding values of ( f(x) ) using the function ( f(x) = \frac{1}{2x} ).

  160. Plot the points ( (x, f(x)) ) on the coordinate plane.

  161. Connect the points smoothlyTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  162. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  163. Determine the behavior as ( x ) approaches positive and negative infinity:

    • As ( x ) approaches positive infinity, ( f(x) ) approaches zero.
    • As ( x ) approaches negative infinity, ( f(x) ) approaches zero.
  164. Plot additional points if necessary:

    • Choose some values for ( x ) and find the corresponding ( y )To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  165. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  166. Choose several values of ( x ) to evaluate the function. You may pick values both greater and less than zero to see the behavior on both sides.

  167. Calculate the corresponding values of ( f(x) ) using the function ( f(x) = \frac{1}{2x} ).

  168. Plot the points ( (x, f(x)) ) on the coordinate plane.

  169. Connect the points smoothly toTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  170. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  171. Determine the behavior as ( x ) approaches positive and negative infinity:

    • As ( x ) approaches positive infinity, ( f(x) ) approaches zero.
    • As ( x ) approaches negative infinity, ( f(x) ) approaches zero.
  172. Plot additional points if necessary:

    • Choose some values for ( x ) and find the corresponding ( y ) valuesTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  173. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  174. Choose several values of ( x ) to evaluate the function. You may pick values both greater and less than zero to see the behavior on both sides.

  175. Calculate the corresponding values of ( f(x) ) using the function ( f(x) = \frac{1}{2x} ).

  176. Plot the points ( (x, f(x)) ) on the coordinate plane.

  177. Connect the points smoothly to formTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  178. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  179. Determine the behavior as ( x ) approaches positive and negative infinity:

    • As ( x ) approaches positive infinity, ( f(x) ) approaches zero.
    • As ( x ) approaches negative infinity, ( f(x) ) approaches zero.
  180. Plot additional points if necessary:

    • Choose some values for ( x ) and find the corresponding ( y ) values byTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  181. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  182. Choose several values of ( x ) to evaluate the function. You may pick values both greater and less than zero to see the behavior on both sides.

  183. Calculate the corresponding values of ( f(x) ) using the function ( f(x) = \frac{1}{2x} ).

  184. Plot the points ( (x, f(x)) ) on the coordinate plane.

  185. Connect the points smoothly to form theTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  186. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  187. Determine the behavior as ( x ) approaches positive and negative infinity:

    • As ( x ) approaches positive infinity, ( f(x) ) approaches zero.
    • As ( x ) approaches negative infinity, ( f(x) ) approaches zero.
  188. Plot additional points if necessary:

    • Choose some values for ( x ) and find the corresponding ( y ) values by evaluatingTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  189. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  190. Choose several values of ( x ) to evaluate the function. You may pick values both greater and less than zero to see the behavior on both sides.

  191. Calculate the corresponding values of ( f(x) ) using the function ( f(x) = \frac{1}{2x} ).

  192. Plot the points ( (x, f(x)) ) on the coordinate plane.

  193. Connect the points smoothly to form the graphTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  194. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  195. Determine the behavior as ( x ) approaches positive and negative infinity:

    • As ( x ) approaches positive infinity, ( f(x) ) approaches zero.
    • As ( x ) approaches negative infinity, ( f(x) ) approaches zero.
  196. Plot additional points if necessary:

    • Choose some values for ( x ) and find the corresponding ( y ) values by evaluating (To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  197. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  198. Choose several values of ( x ) to evaluate the function. You may pick values both greater and less than zero to see the behavior on both sides.

  199. Calculate the corresponding values of ( f(x) ) using the function ( f(x) = \frac{1}{2x} ).

  200. Plot the points ( (x, f(x)) ) on the coordinate plane.

  201. Connect the points smoothly to form the graph.

RememberTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  1. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  2. Determine the behavior as ( x ) approaches positive and negative infinity:

    • As ( x ) approaches positive infinity, ( f(x) ) approaches zero.
    • As ( x ) approaches negative infinity, ( f(x) ) approaches zero.
  3. Plot additional points if necessary:

    • Choose some values for ( x ) and find the corresponding ( y ) values by evaluating ( fTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  4. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  5. Choose several values of ( x ) to evaluate the function. You may pick values both greater and less than zero to see the behavior on both sides.

  6. Calculate the corresponding values of ( f(x) ) using the function ( f(x) = \frac{1}{2x} ).

  7. Plot the points ( (x, f(x)) ) on the coordinate plane.

  8. Connect the points smoothly to form the graph.

Remember thatTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  1. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  2. Determine the behavior as ( x ) approaches positive and negative infinity:

    • As ( x ) approaches positive infinity, ( f(x) ) approaches zero.
    • As ( x ) approaches negative infinity, ( f(x) ) approaches zero.
  3. Plot additional points if necessary:

    • Choose some values for ( x ) and find the corresponding ( y ) values by evaluating ( f(x)To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  4. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  5. Choose several values of ( x ) to evaluate the function. You may pick values both greater and less than zero to see the behavior on both sides.

  6. Calculate the corresponding values of ( f(x) ) using the function ( f(x) = \frac{1}{2x} ).

  7. Plot the points ( (x, f(x)) ) on the coordinate plane.

  8. Connect the points smoothly to form the graph.

Remember that theTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  1. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  2. Determine the behavior as ( x ) approaches positive and negative infinity:

    • As ( x ) approaches positive infinity, ( f(x) ) approaches zero.
    • As ( x ) approaches negative infinity, ( f(x) ) approaches zero.
  3. Plot additional points if necessary:

    • Choose some values for ( x ) and find the corresponding ( y ) values by evaluating ( f(x) \To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  4. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  5. Choose several values of ( x ) to evaluate the function. You may pick values both greater and less than zero to see the behavior on both sides.

  6. Calculate the corresponding values of ( f(x) ) using the function ( f(x) = \frac{1}{2x} ).

  7. Plot the points ( (x, f(x)) ) on the coordinate plane.

  8. Connect the points smoothly to form the graph.

Remember that the graphTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  1. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  2. Determine the behavior as ( x ) approaches positive and negative infinity:

    • As ( x ) approaches positive infinity, ( f(x) ) approaches zero.
    • As ( x ) approaches negative infinity, ( f(x) ) approaches zero.
  3. Plot additional points if necessary:

    • Choose some values for ( x ) and find the corresponding ( y ) values by evaluating ( f(x) ). To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  4. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  5. Choose several values of ( x ) to evaluate the function. You may pick values both greater and less than zero to see the behavior on both sides.

  6. Calculate the corresponding values of ( f(x) ) using the function ( f(x) = \frac{1}{2x} ).

  7. Plot the points ( (x, f(x)) ) on the coordinate plane.

  8. Connect the points smoothly to form the graph.

Remember that the graph willTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  1. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  2. Determine the behavior as ( x ) approaches positive and negative infinity:

    • As ( x ) approaches positive infinity, ( f(x) ) approaches zero.
    • As ( x ) approaches negative infinity, ( f(x) ) approaches zero.
  3. Plot additional points if necessary:

    • Choose some values for ( x ) and find the corresponding ( y ) values by evaluating ( f(x) ). To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  4. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  5. Choose several values of ( x ) to evaluate the function. You may pick values both greater and less than zero to see the behavior on both sides.

  6. Calculate the corresponding values of ( f(x) ) using the function ( f(x) = \frac{1}{2x} ).

  7. Plot the points ( (x, f(x)) ) on the coordinate plane.

  8. Connect the points smoothly to form the graph.

Remember that the graph will approach theTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  1. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  2. Determine the behavior as ( x ) approaches positive and negative infinity:

    • As ( x ) approaches positive infinity, ( f(x) ) approaches zero.
    • As ( x ) approaches negative infinity, ( f(x) ) approaches zero.
  3. Plot additional points if necessary:

    • Choose some values for ( x ) and find the corresponding ( y ) values by evaluating ( f(x) ).
    • ForTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  4. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  5. Choose several values of ( x ) to evaluate the function. You may pick values both greater and less than zero to see the behavior on both sides.

  6. Calculate the corresponding values of ( f(x) ) using the function ( f(x) = \frac{1}{2x} ).

  7. Plot the points ( (x, f(x)) ) on the coordinate plane.

  8. Connect the points smoothly to form the graph.

Remember that the graph will approach the xTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  1. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  2. Determine the behavior as ( x ) approaches positive and negative infinity:

    • As ( x ) approaches positive infinity, ( f(x) ) approaches zero.
    • As ( x ) approaches negative infinity, ( f(x) ) approaches zero.
  3. Plot additional points if necessary:

    • Choose some values for ( x ) and find the corresponding ( y ) values by evaluating ( f(x) ).
    • For exampleTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  4. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  5. Choose several values of ( x ) to evaluate the function. You may pick values both greater and less than zero to see the behavior on both sides.

  6. Calculate the corresponding values of ( f(x) ) using the function ( f(x) = \frac{1}{2x} ).

  7. Plot the points ( (x, f(x)) ) on the coordinate plane.

  8. Connect the points smoothly to form the graph.

Remember that the graph will approach the x-axisTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  1. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  2. Determine the behavior as ( x ) approaches positive and negative infinity:

    • As ( x ) approaches positive infinity, ( f(x) ) approaches zero.
    • As ( x ) approaches negative infinity, ( f(x) ) approaches zero.
  3. Plot additional points if necessary:

    • Choose some values for ( x ) and find the corresponding ( y ) values by evaluating ( f(x) ).
    • For example,To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  4. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  5. Choose several values of ( x ) to evaluate the function. You may pick values both greater and less than zero to see the behavior on both sides.

  6. Calculate the corresponding values of ( f(x) ) using the function ( f(x) = \frac{1}{2x} ).

  7. Plot the points ( (x, f(x)) ) on the coordinate plane.

  8. Connect the points smoothly to form the graph.

Remember that the graph will approach the x-axis butTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  1. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  2. Determine the behavior as ( x ) approaches positive and negative infinity:

    • As ( x ) approaches positive infinity, ( f(x) ) approaches zero.
    • As ( x ) approaches negative infinity, ( f(x) ) approaches zero.
  3. Plot additional points if necessary:

    • Choose some values for ( x ) and find the corresponding ( y ) values by evaluating ( f(x) ).
    • For example, whenTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  4. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  5. Choose several values of ( x ) to evaluate the function. You may pick values both greater and less than zero to see the behavior on both sides.

  6. Calculate the corresponding values of ( f(x) ) using the function ( f(x) = \frac{1}{2x} ).

  7. Plot the points ( (x, f(x)) ) on the coordinate plane.

  8. Connect the points smoothly to form the graph.

Remember that the graph will approach the x-axis but neverTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  1. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  2. Determine the behavior as ( x ) approaches positive and negative infinity:

    • As ( x ) approaches positive infinity, ( f(x) ) approaches zero.
    • As ( x ) approaches negative infinity, ( f(x) ) approaches zero.
  3. Plot additional points if necessary:

    • Choose some values for ( x ) and find the corresponding ( y ) values by evaluating ( f(x) ).
    • For example, when (To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  4. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  5. Choose several values of ( x ) to evaluate the function. You may pick values both greater and less than zero to see the behavior on both sides.

  6. Calculate the corresponding values of ( f(x) ) using the function ( f(x) = \frac{1}{2x} ).

  7. Plot the points ( (x, f(x)) ) on the coordinate plane.

  8. Connect the points smoothly to form the graph.

Remember that the graph will approach the x-axis but never actuallyTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  1. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  2. Determine the behavior as ( x ) approaches positive and negative infinity:

    • As ( x ) approaches positive infinity, ( f(x) ) approaches zero.
    • As ( x ) approaches negative infinity, ( f(x) ) approaches zero.
  3. Plot additional points if necessary:

    • Choose some values for ( x ) and find the corresponding ( y ) values by evaluating ( f(x) ).
    • For example, when ( xTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  4. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  5. Choose several values of ( x ) to evaluate the function. You may pick values both greater and less than zero to see the behavior on both sides.

  6. Calculate the corresponding values of ( f(x) ) using the function ( f(x) = \frac{1}{2x} ).

  7. Plot the points ( (x, f(x)) ) on the coordinate plane.

  8. Connect the points smoothly to form the graph.

Remember that the graph will approach the x-axis but never actually touchTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  1. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  2. Determine the behavior as ( x ) approaches positive and negative infinity:

    • As ( x ) approaches positive infinity, ( f(x) ) approaches zero.
    • As ( x ) approaches negative infinity, ( f(x) ) approaches zero.
  3. Plot additional points if necessary:

    • Choose some values for ( x ) and find the corresponding ( y ) values by evaluating ( f(x) ).
    • For example, when ( x =To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  4. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  5. Choose several values of ( x ) to evaluate the function. You may pick values both greater and less than zero to see the behavior on both sides.

  6. Calculate the corresponding values of ( f(x) ) using the function ( f(x) = \frac{1}{2x} ).

  7. Plot the points ( (x, f(x)) ) on the coordinate plane.

  8. Connect the points smoothly to form the graph.

Remember that the graph will approach the x-axis but never actually touch itTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  1. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  2. Determine the behavior as ( x ) approaches positive and negative infinity:

    • As ( x ) approaches positive infinity, ( f(x) ) approaches zero.
    • As ( x ) approaches negative infinity, ( f(x) ) approaches zero.
  3. Plot additional points if necessary:

    • Choose some values for ( x ) and find the corresponding ( y ) values by evaluating ( f(x) ).
    • For example, when ( x = To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  4. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  5. Choose several values of ( x ) to evaluate the function. You may pick values both greater and less than zero to see the behavior on both sides.

  6. Calculate the corresponding values of ( f(x) ) using the function ( f(x) = \frac{1}{2x} ).

  7. Plot the points ( (x, f(x)) ) on the coordinate plane.

  8. Connect the points smoothly to form the graph.

Remember that the graph will approach the x-axis but never actually touch it asTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  1. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  2. Determine the behavior as ( x ) approaches positive and negative infinity:

    • As ( x ) approaches positive infinity, ( f(x) ) approaches zero.
    • As ( x ) approaches negative infinity, ( f(x) ) approaches zero.
  3. Plot additional points if necessary:

    • Choose some values for ( x ) and find the corresponding ( y ) values by evaluating ( f(x) ).
    • For example, when ( x = 1To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  4. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  5. Choose several values of ( x ) to evaluate the function. You may pick values both greater and less than zero to see the behavior on both sides.

  6. Calculate the corresponding values of ( f(x) ) using the function ( f(x) = \frac{1}{2x} ).

  7. Plot the points ( (x, f(x)) ) on the coordinate plane.

  8. Connect the points smoothly to form the graph.

Remember that the graph will approach the x-axis but never actually touch it as (To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  1. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  2. Determine the behavior as ( x ) approaches positive and negative infinity:

    • As ( x ) approaches positive infinity, ( f(x) ) approaches zero.
    • As ( x ) approaches negative infinity, ( f(x) ) approaches zero.
  3. Plot additional points if necessary:

    • Choose some values for ( x ) and find the corresponding ( y ) values by evaluating ( f(x) ).
    • For example, when ( x = 1 \To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  4. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  5. Choose several values of ( x ) to evaluate the function. You may pick values both greater and less than zero to see the behavior on both sides.

  6. Calculate the corresponding values of ( f(x) ) using the function ( f(x) = \frac{1}{2x} ).

  7. Plot the points ( (x, f(x)) ) on the coordinate plane.

  8. Connect the points smoothly to form the graph.

Remember that the graph will approach the x-axis but never actually touch it as ( xTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  1. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  2. Determine the behavior as ( x ) approaches positive and negative infinity:

    • As ( x ) approaches positive infinity, ( f(x) ) approaches zero.
    • As ( x ) approaches negative infinity, ( f(x) ) approaches zero.
  3. Plot additional points if necessary:

    • Choose some values for ( x ) and find the corresponding ( y ) values by evaluating ( f(x) ).
    • For example, when ( x = 1 ),To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  4. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  5. Choose several values of ( x ) to evaluate the function. You may pick values both greater and less than zero to see the behavior on both sides.

  6. Calculate the corresponding values of ( f(x) ) using the function ( f(x) = \frac{1}{2x} ).

  7. Plot the points ( (x, f(x)) ) on the coordinate plane.

  8. Connect the points smoothly to form the graph.

Remember that the graph will approach the x-axis but never actually touch it as ( x )To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  1. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  2. Determine the behavior as ( x ) approaches positive and negative infinity:

    • As ( x ) approaches positive infinity, ( f(x) ) approaches zero.
    • As ( x ) approaches negative infinity, ( f(x) ) approaches zero.
  3. Plot additional points if necessary:

    • Choose some values for ( x ) and find the corresponding ( y ) values by evaluating ( f(x) ).
    • For example, when ( x = 1 ), ( fTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  4. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  5. Choose several values of ( x ) to evaluate the function. You may pick values both greater and less than zero to see the behavior on both sides.

  6. Calculate the corresponding values of ( f(x) ) using the function ( f(x) = \frac{1}{2x} ).

  7. Plot the points ( (x, f(x)) ) on the coordinate plane.

  8. Connect the points smoothly to form the graph.

Remember that the graph will approach the x-axis but never actually touch it as ( x ) approachesTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  1. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  2. Determine the behavior as ( x ) approaches positive and negative infinity:

    • As ( x ) approaches positive infinity, ( f(x) ) approaches zero.
    • As ( x ) approaches negative infinity, ( f(x) ) approaches zero.
  3. Plot additional points if necessary:

    • Choose some values for ( x ) and find the corresponding ( y ) values by evaluating ( f(x) ).
    • For example, when ( x = 1 ), ( f(To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  4. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  5. Choose several values of ( x ) to evaluate the function. You may pick values both greater and less than zero to see the behavior on both sides.

  6. Calculate the corresponding values of ( f(x) ) using the function ( f(x) = \frac{1}{2x} ).

  7. Plot the points ( (x, f(x)) ) on the coordinate plane.

  8. Connect the points smoothly to form the graph.

Remember that the graph will approach the x-axis but never actually touch it as ( x ) approaches positiveTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  1. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  2. Determine the behavior as ( x ) approaches positive and negative infinity:

    • As ( x ) approaches positive infinity, ( f(x) ) approaches zero.
    • As ( x ) approaches negative infinity, ( f(x) ) approaches zero.
  3. Plot additional points if necessary:

    • Choose some values for ( x ) and find the corresponding ( y ) values by evaluating ( f(x) ).
    • For example, when ( x = 1 ), ( f(1To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  4. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  5. Choose several values of ( x ) to evaluate the function. You may pick values both greater and less than zero to see the behavior on both sides.

  6. Calculate the corresponding values of ( f(x) ) using the function ( f(x) = \frac{1}{2x} ).

  7. Plot the points ( (x, f(x)) ) on the coordinate plane.

  8. Connect the points smoothly to form the graph.

Remember that the graph will approach the x-axis but never actually touch it as ( x ) approaches positive orTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  1. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  2. Determine the behavior as ( x ) approaches positive and negative infinity:

    • As ( x ) approaches positive infinity, ( f(x) ) approaches zero.
    • As ( x ) approaches negative infinity, ( f(x) ) approaches zero.
  3. Plot additional points if necessary:

    • Choose some values for ( x ) and find the corresponding ( y ) values by evaluating ( f(x) ).
    • For example, when ( x = 1 ), ( f(1)To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  4. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  5. Choose several values of ( x ) to evaluate the function. You may pick values both greater and less than zero to see the behavior on both sides.

  6. Calculate the corresponding values of ( f(x) ) using the function ( f(x) = \frac{1}{2x} ).

  7. Plot the points ( (x, f(x)) ) on the coordinate plane.

  8. Connect the points smoothly to form the graph.

Remember that the graph will approach the x-axis but never actually touch it as ( x ) approaches positive or negativeTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  1. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  2. Determine the behavior as ( x ) approaches positive and negative infinity:

    • As ( x ) approaches positive infinity, ( f(x) ) approaches zero.
    • As ( x ) approaches negative infinity, ( f(x) ) approaches zero.
  3. Plot additional points if necessary:

    • Choose some values for ( x ) and find the corresponding ( y ) values by evaluating ( f(x) ).
    • For example, when ( x = 1 ), ( f(1) =To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  4. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  5. Choose several values of ( x ) to evaluate the function. You may pick values both greater and less than zero to see the behavior on both sides.

  6. Calculate the corresponding values of ( f(x) ) using the function ( f(x) = \frac{1}{2x} ).

  7. Plot the points ( (x, f(x)) ) on the coordinate plane.

  8. Connect the points smoothly to form the graph.

Remember that the graph will approach the x-axis but never actually touch it as ( x ) approaches positive or negative infinityTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  1. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  2. Determine the behavior as ( x ) approaches positive and negative infinity:

    • As ( x ) approaches positive infinity, ( f(x) ) approaches zero.
    • As ( x ) approaches negative infinity, ( f(x) ) approaches zero.
  3. Plot additional points if necessary:

    • Choose some values for ( x ) and find the corresponding ( y ) values by evaluating ( f(x) ).
    • For example, when ( x = 1 ), ( f(1) = \To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  4. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  5. Choose several values of ( x ) to evaluate the function. You may pick values both greater and less than zero to see the behavior on both sides.

  6. Calculate the corresponding values of ( f(x) ) using the function ( f(x) = \frac{1}{2x} ).

  7. Plot the points ( (x, f(x)) ) on the coordinate plane.

  8. Connect the points smoothly to form the graph.

Remember that the graph will approach the x-axis but never actually touch it as ( x ) approaches positive or negative infinity.To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  1. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  2. Determine the behavior as ( x ) approaches positive and negative infinity:

    • As ( x ) approaches positive infinity, ( f(x) ) approaches zero.
    • As ( x ) approaches negative infinity, ( f(x) ) approaches zero.
  3. Plot additional points if necessary:

    • Choose some values for ( x ) and find the corresponding ( y ) values by evaluating ( f(x) ).
    • For example, when ( x = 1 ), ( f(1) = \fracTo graph the function ( f(x) = \frac{1}{2x} ), follow these steps:
  4. Identify the domain of the function, which is all real numbers except ( x = 0 ) since division by zero is undefined.

  5. Choose several values of ( x ) to evaluate the function. You may pick values both greater and less than zero to see the behavior on both sides.

  6. Calculate the corresponding values of ( f(x) ) using the function ( f(x) = \frac{1}{2x} ).

  7. Plot the points ( (x, f(x)) ) on the coordinate plane.

  8. Connect the points smoothly to form the graph.

Remember that the graph will approach the x-axis but never actually touch it as ( x ) approaches positive or negative infinity.To graph the function ( f(x) = \frac{1}{2x} ), follow these steps:

  1. Identify the vertical asymptote:

    • The function ( f(x) ) has a vertical asymptote at ( x = 0 ) because the denominator cannot equal zero.
  2. Determine the behavior as ( x ) approaches positive and negative infinity:

    • As ( x ) approaches positive infinity, ( f(x) ) approaches zero.
    • As ( x ) approaches negative infinity, ( f(x) ) approaches zero.
  3. Plot additional points if necessary:

    • Choose some values for ( x ) and find the corresponding ( y ) values by evaluating ( f(x) ).
    • For example, when ( x = 1 ), ( f(1) = \frac{1}{2(1)} = \frac{1}{2} ).
    • Similarly, when ( x = -1 ), ( f(-1) = \frac{1}{2(-1)} = -\frac{1}{2} ).
  4. Plot the points on the graph and draw the curve:

    • Plot the vertical asymptote at ( x = 0 ).
    • Plot the additional points you found.
    • Draw the curve that approaches the asymptote as ( x ) approaches zero and approaches zero as ( x ) approaches positive and negative infinity.
  5. Label the axes and any important points on the graph.

  6. Optionally, you can use a graphing calculator or software to plot the graph accurately.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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