How do you graph and find the discontinuities of #f(x)=1/x -4#?

Question

Kennedy Adams · Accepted Answer

Discontinuity point is #x=0# Your graph will be This You will observe that the discontinuity point is #x=0#.

Genesis Allen · Answer

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

1. Determine the vertical asymptotes: Set the denominator equal to zero and solve for x. In this case, solve the equation x = 0. The vertical asymptote is x = 0.

2. Determine the horizontal asymptote: Compare the degrees of the numerator and denominator. Since the degree of the numerator is 0 and the degree of the denominator is 1, the horizontal asymptote is y = 0.

3. Find the x-intercept: Set the function equal to zero and solve for x. In this case, solve the equation 1/x - 4 = 0. Simplify to x = 1/4. The x-intercept is (1/4, 0).

4. Find the y-intercept: Substitute x = 0 into the function. In this case, f(0) = 1/0 - 4, which is undefined. Therefore, there is no y-intercept.

5. Plot the points: Plot the vertical asymptote at x = 0, the horizontal asymptote at y = 0, and the x-intercept at (1/4, 0).

6. Determine the behavior of the function: As x approaches positive or negative infinity, the function approaches the horizontal asymptote y = 0.

7. Identify any discontinuities: The function has a vertical asymptote at x = 0, which means it is discontinuous at x = 0.

8. Connect the points: Draw a curve that approaches the vertical asymptote at x = 0 and approaches the horizontal asymptote y = 0 as x approaches positive or negative infinity.

This completes the graphing and identification of discontinuities for the function f(x) = 1/x - 4.