Michigan Algebra II KHauck

Points where the graph cross the x-axis are the x-intercepts, where y = 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)