Rational Functions
Instructions
- The introductory videos below explain the concepts in this section.
- This page also includes exercises that you should attempt to solve yourself. You can check your answers and watch the videos explaining how to solve the exercises.
- When you are done, you can use the graph to pick another section or use the buttons to go to the next section.
Learning Objectives
- The parent functions \(y=\frac{1}{x}\) and \(y=\frac{1}{x^2}\) of rational functions and their properties including the graph, domain, range, vertical asymptotes, and end behavior
- How to determine the horizontal asymptotes and end behavior of rational functions by comparing the degree of the polynomial in the numerator with the degree of the polynomial in the denominator
Concept Video(s)
Exercises
1.
- Horizontal Asymptote of \(y=0\) as \(x\rightarrow \pm \infty\)
- Horizontal Asymptote of \(y=\dfrac{1}{5}\) as \(x\rightarrow \pm \infty\)
2.
\(y\rightarrow \infty\) as \(x\rightarrow -\infty \) and \(y\rightarrow -\infty\) as \(x\rightarrow \infty\); No Horizontal Asymptote