Question

Find all intercepts of the following function. g(x)=(1)/(x-4)

Answer 1

To find the intercepts of the function g(x) = 1/(x-4), we need to find the x-intercept and the y-intercept. The x-intercept does not exist, and the y-intercept is (0, -1/4).

Step-by-step explanation:

To find the intercepts of the function g(x) = 1/(x-4), we need to find the x-intercept and the y-intercept.

To find the x-intercept, we set y = 0 and solve for x:

1. 0 = 1/(x-4)
2. Multiply both sides by (x-4): 0 = 1
3. This equation has no solution, so there is no x-intercept.

To find the y-intercept, we set x = 0 and solve for y:

1. y = 1/(0-4)
2. Perform the subtraction: y = 1/(-4)
3. Calculate the division: y = -1/4

Therefore, the y-intercept is (0, -1/4).