# Graphing Rational Functions

Time to put all of it together. Here are some steps that sum up the video for graphing rational functions:

- Find any intercepts. Remember to find \(x\)-intercepts by setting the factors in the numerator equal to zero. To find any \(y\)-intercepts evaluate the whole function for \(x=0\).
- Find the vertical asymptotes by setting the denominator equal to zero and solving.
- Find any horizontal asymptotes.
- Draw the asymptotes using dotted lines. The vertical asymptotes divide the graph into sections.
- Find some points in each section and sketch the graph.

Pick two of the functions below.

- Find all the key features we have discussed (asymptotes, holes, intercepts).
- Sketch a graph of the function.
- Check answers with Desmos or another graphing utility. Key features are on solution page.

- \(f(x)=\dfrac{1}{3x^2+3x-18}\)
- \(f(x)=\dfrac{x-3}{x-4}\)
- \(f(x)=\dfrac{x^3-x^2-8}{-4x^2-4x+24}\)
- \(f(x)=\dfrac{x-5}{-5x-20}\)
- \(f(x)=\dfrac{4x^2-16x}{x^2-3x-4}\)
- \(f(x)=\dfrac{3x^2+15x+18}{x^2+5x+6}\)