# Section 3.5

## Table of Contents

Summary of Curve Sketching

The examples in this section use everything we’ve learned for the previous four sections all at once. As a result, each video is quite long. Pause when you need to and ask any questions that you have!

## Curve Sketching Guidelines #

Guidelines: A Sketching Checklist (and they really are guidelines, not hard rules)

- Find domain
- Find intercepts
- Does the function have symmetry? (Even / odd / periodic?)
- Find asymptotes: vertical and horizontal
- Find intervals of increasing and decreasing
- Find local maximum and minimum values
- Find concavity and points of inflection
- Sketch the curve.

### Example #

Sketch $$ f(x) = \dfrac{2x^2}{x^2-1} $$

### Example #

Sketch the graph of $$ y = \sqrt[3]{x^2-1} $$