How to find the x intercept 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. 

Finding x-intercepts

Points where the graph cross the x-axis are the x-intercepts, wherey = 0. The x-intercepts of a function are also known as the zeros or real roots of the corresponding equation. In the case of rational functions, x-intercepts exist when the numerator equals zero.

To determine the x-intercepts of the function, set the numerator equal to zero and solve for x. Eliminate the excluded values because the function will be undefined and will not cross the x-axis.

Example 1 Find the x-intercepts of the function.

Step 1. Simplify the function completely.

Since x = -4 is an excluded value, it can not be an x-intercept.

Step 2. Using the Zero Product Property, set the factor(s) in the numerator equal to zero and solve.

or

or

x-intercepts: (2, 0) or (1, 0)

Home > Math > Calculus > Finding Intercepts of Rational Fractions

Intercepts are the points at which a graph crosses either the x or y axis, and they are very useful in sketching functions.

To find the y-intercept(s) (the point where the graph crosses the y-axis), substitute in 0 for x and solve for y or f(x).

To find the x-intercept(s) (the point where the graph crosses the x-axis – also known as zeros), substitute in 0 for y and solve for x.

Examples: Find the intercepts of the function given.

To find the y-intercept, we must substitute in 0 for each x:

And then simplify:

There is a y-intercept at

To find the x-intercept, we must substitute in 0 for y or f(x):

And then solve by cross-multiplying:

0 = x + 10

x = -10

There is a y-intercept at

To find the y-intercept, we must substitute in 0 for each x:

And then simplify:

There is a y-intercept at

To find the x-intercept, we must substitute in 0 for y or f(x):

And then solve by cross-multiplying:

We must now solve the quadratic either by factoring or by using the quadratic formula.
We can factor this trinomial, so we'll use that method:

There are y-intercepts at

Note: Not all rational functions have both an x or y intercept. If you cannot find a real solution, then it does not have that intercept.

Practice: Find the x and y intercepts of each rational function:

Answers: 1)x-int.

2) x-int. (4, 0) y-int.

3) x-int. (-2, 0) and (5, 0) y-int

What is the x

How do you find the Y and X

How do you find the x