Zeros of a rational function

In this lesson, we learn how to find the zeros and asymptotes of a rational function. By setting the numerator equal to zero, we can find the values of x that make the function zero, which correspond to where the graph crosses the x-axis. Additionally, we can find the vertical asymptotes by setting the denominator equal to zero. Through an example problem, we see how to factor and solve for x to determine the zeros, which can help us better understand the behavior of the function.

Given a rational functions that consists of a ratio of rational functions, setting the top expression (the numerator) equal to zero and then solving for x allows you to find values of x that cause the value of the function (y-value) to equal zero. When graphing, this is where the graph you are drawing will cross the x-axis.

• What are the zeroes of a rational function?
• How do you find the zeroes of a rational function?
• What are the zeroes of f(x) = (3x^2 - 27)/(x^2 - 36)?