How do you graph #f(x)=1/x -4#?

Question

Eli Assouline · Accepted Answer

undefined To graph the function f(x) = 1/x - 4, follow these steps:

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

2. Find the y-intercept by substituting x = 0 into the equation: f(0) = 1/0 - 4. Since division by zero is undefined, there is no y-intercept.

3. Determine the vertical asymptote(s) by setting the denominator equal to zero and solving for x: x ≠ 0.

4. Find the horizontal asymptote by analyzing the behavior of the function as x approaches positive or negative infinity. In this case, the horizontal asymptote is y = -4.

5. Choose some x-values to evaluate the function and find corresponding y-values. Plot these points on the graph.

6. Draw the graph, making sure it approaches the vertical asymptote(s) and the horizontal asymptote as x approaches infinity or negative infinity.

Note: The graph will be a hyperbola with a vertical asymptote at x = 0 and a horizontal asymptote at y = -4.

Eva Abramson · Answer

Assign a number to x to find #f(x)# If x is 1, #f(x)=-3# If x is 2, #f(x) = -3.5# etc. Note that #f(x)# is not defined when #x=0# graph{(1/x)-4 [-10, 10, -5, 5]}