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College Algebra Tutorial 40: Graphs of Rational Functions

Learning Objectives After completing this tutorial, you should be able to: 1. 2. 3. 4.

Find the domain of a rational function. Find the vertical asymptote(s) of a rational function. Find the horizontal asymptote of a rational function. Find the oblique or slant asymptote of a rational function.

5. Graph a rational function.

Introduction In this tutorial we will be looking at several aspects of rational functions. First we will revisit the concept of domain. On rational functions, we need to be careful that we don't use values of x that cause our denominator to be zero. If you need a review on domain, feel free to go to Tutorial 30: Introductions to Functions. Next, we look at vertical, horizontal and slant asymptotes. Basically an asymptote is an imaginary line that the curve of the function gets very close to or approaches. In the end, we put it all together and graph rational functions. Sounds like fun, you better get to it!!!

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