# Gizmo of the Week: General Form of a Rational Function

A rational function is a ratio of two polynomials. Like any fraction, a rational function is undefined when its denominator equals zero.

So what does that look like on the graph, where x equals a root of the denominator? What happens to the y-values as x approaches those roots?

In the General Form of a Rational Function Gizmo, students can create and graph a wide variety of rational functions, with up to three linear factors in both the numerator and denominator.

With the help of the newly updated Lesson Materials, they can determine the asymptotes and domains, find the x-intercepts, explore the end behavior, and even take an interesting look at the near-origin behavior of these graphs.