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.