Section 3.6 – Curve Sketching

Guidelines for sketching a Curve The following checklist is intended as a guide to sketching a curve by hand without a calculator. Not every item is relevant to every function. But the guidelines provide all the information needed to make a sketch that displays the most important aspects of the function. 1.Domain 2.x and y-intercept(s) 3.Symmetry 4.Horizontal, Vertical, and Slant Asymptotes 5.Intervals of Increase or Decrease 6.Local Maximum and Minimum Values 7.Concavity and Points of Inflection Once you have completed the checklist, sketch the graph.

Example 1 Without a calculator, sketch the graph of the function below by finding everything on the checklist (if it exists). 1.Domain 2.x and y-intercept(s) 3.Symmetry 4.Horizontal, Vertical, and Slant Asymptotes 5.Intervals of Increase or Decrease 6.Local Maximum and Minimum Values 7.Concavity and Points of Inflection Mr. Wells will approximate irrational numbers for you.

Answer to Example 1 Even Function.

Example 2 Without a calculator, sketch the graph of the function below by finding everything on the checklist (if it exists). 1.Domain 2.x and y-intercept(s) 3.Symmetry 4.Horizontal, Vertical, and Slant Asymptotes 5.Intervals of Increase or Decrease 6.Local Maximum and Minimum Values 7.Concavity and Points of Inflection Mr. Wells will approximate irrational numbers for you.

Answer to Example 2 Inflection Points

Example 3 Without a calculator, sketch the graph of the function below by finding everything on the checklist (if it exists). 1.Domain 2.x and y-intercept(s) 3.Symmetry 4.Horizontal, Vertical, and Slant Asymptotes 5.Intervals of Increase or Decrease 6.Local Maximum and Minimum Values 7.Concavity and Points of Inflection Mr. Wells will approximate irrational numbers for you.

Answer to Example 3 y = x Odd Function.

Example 4 Without a calculator, sketch the graph of the function below by finding everything on the checklist (if it exists). 1.Domain 2.x and y-intercept(s) 3.Symmetry 4.Horizontal, Vertical, and Slant Asymptotes 5.Intervals of Increase or Decrease 6.Local Maximum and Minimum Values 7.Concavity and Points of Inflection Mr. Wells will approximate irrational numbers for you.

Answer to Example 4 Inflection Points

Without a calculator, sketch the graph of the function below by finding everything on the checklist (if it exists). 1.Domain 2.x and y-intercept(s) 3.Symmetry 4.Horizontal, Vertical, and Slant Asymptotes 5.Intervals of Increase or Decrease 6.Local Maximum and Minimum Values 7.Concavity and Points of Inflection Example 5

Answer to Example 5 y = x x = 0 Odd Function.