How to Sketch Curves

Your textbook summarizes most of your tools for sketching curves. What makes my summary any different? It’s in the order you’d actually check these things, not just the order they happen to be in the book.

Use these techniques to sketch a graph of a function:

1. transformations from a function with a known graph
2. domain and range
3. continuity
4. symmetry
5. intercepts
6. asymptotes: vertical, horizontal, and slant
7. leading coefficient test for polynomial, or infinite limits at infinity for any function
8. regions where function is increasing or decreasing
9. relative extrema
10. concavity and points of inflection

You won’t use all of these techniques for every function, but see where your investigation takes you.