Sketching Curves
(Lecture Notes for L-H-E Calculus 7e section 3.6)

Page 202 of 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; and it shows specific page numbers, not just section numbers.

Use these techniques to sketch a graph of a function:

1. transformations (page 23) from a function with a known graph
2. domain and range (page 21)
3. continuity (page 68)
4. symmetry (page 5)
5. intercepts (page 4)
6. asymptotes: vertical (page 62), horizontal (page 193), and slant (page 204)
7. leading coefficient test for polynomials (page 24), or infinite limits at infinity (page 198) for any function
8. regions where function is increasing or decreasing (page 174)
9. relative extrema (pages 176, 188)
10. concavity (page 185) and points of inflection (page 187)

You won’t use all of these techniques for every function, but see where your investigation takes you. The Guidelines box on page 202 is a super-fast summary of what to look for.

Examples: page 208 problems 16, 32, 68, 70