How to find the x and y-intercepts of a rational function?

A rational function is expressed in the form of p(x) / q(x), where q(x) is not equal to zero.

Answer: To find the x-intercept of a rational function, we substitute y = 0 in the function and find the corresponding value of x, and to find the y-intercept of a rational function, we substitute x = 0 in the function and find the corresponding value of y. 

Let us proceed step by step.

Explanation:

The x-intercept of a line is that point where it cuts the x-axis of the graph, and the y-intercept of a line is that point where it cuts the y-axis of the graph.

Let us consider a rational function given by f (x) = (x + 10) / (x - 5) -----(1)

We will try to find the x-intercept and y-intercept for the given rational function.

To find the y-intercept, we must substitute x = 0 in (1):

After substituting the value of x as 0 in equation 1 we get, f (x) = -2

Therefore, the y-intercept of rational function f (x) = (x + 10) / (x - 5) is (0, -2)

To find the x-intercept, we must substitute y=0, that is, f(x) = 0

After substituting the value of y as 0 in equation (1), we get, x = -10

Therefore x-intercept will be (-10, 0)

Hence, to find the x-intercept of a rational function, we substitute y = 0 in the function and find the corresponding value of x, and to find the y-intercept of a rational function, we substitute x = 0 in the function and find the corresponding value of y.