Graphing a Rational Function

A rational function is the quotient of 2 polynomials.

There are five essential steps in order to graph a rational function.

Step #1 Find all of the asymptotes & draw the asymptotes as a dashed line. Recall, asymptotes are the limits of the curves of a function.

Step #2 Find and plot any intercepts that exist. Recall, the x-intercept can be found by setting y= 0 and solving for x and the y-intercept can be found by setting x= 0 and solving for y.

Step #3 Find and plot several other points on the graph. The points will give us a good idea of what the graph of the rational function will look like.

Step #4 Draw curves through the points, approaching the asymptotes. Recall, the curve will never cross the asymptotes. If the curve does, there are algebraic errors in the previous steps. And you should check your work.

Yay! We know how to graph a rational function.