How do you graph #y=7/x+3# using asymptotes, intercepts, end behavior?

Answer 1

horizontal asymptote at #y=3#
Vertical asymptote at #x=0#

If you look at the equation, there is one evident asymptote which is when #x=0#,it's a vertical asymptote since #x≠0# THe other one is when #xrarr+-oo#, # yrarr3# So #y=3# is a horizontal asymptote To caculate the intercept with the x axis, put #y=0# #0=7/x +3# So #7/x=-3 # and #x=-7/3# See Graph graph{3+(7/x) [-20, 20, -10, 10]}
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Answer 2

To graph the function ( y = \frac{7}{x + 3} ), you can follow these steps:

  1. Vertical Asymptote: Set the denominator equal to zero to find the vertical asymptote. In this case, ( x + 3 = 0 ) gives ( x = -3 ) as the vertical asymptote.

  2. Horizontal Asymptote: As ( x ) approaches positive or negative infinity, the function approaches zero. So, there is a horizontal asymptote at ( y = 0 ).

  3. Intercepts: To find the ( y )-intercept, set ( x = 0 ) and solve for ( y ). [ y = \frac{7}{0 + 3} = \frac{7}{3} ] So, the ( y )-intercept is ( \left(0, \frac{7}{3}\right) ). There is no ( x )-intercept.

  4. End Behavior: As ( x ) approaches positive infinity, ( y ) approaches zero. As ( x ) approaches negative infinity, ( y ) also approaches zero.

  5. Plotting:

    • Plot the vertical asymptote at ( x = -3 ).
    • Plot the horizontal asymptote at ( y = 0 ).
    • Plot the ( y )-intercept at ( \left(0, \frac{7}{3}\right) ).
    • As ( x ) approaches ( -3 ) from the left, ( y ) approaches negative infinity, and as ( x ) approaches ( -3 ) from the right, ( y ) approaches positive infinity.
    • Draw the curve approaching the asymptotes, avoiding crossing them.

By following these steps, you can graph the function ( y = \frac{7}{x + 3} ) accurately, showing its asymptotes, intercepts, and end behavior.

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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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