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Section 3.6 – Curve Sketching

This guide provides a comprehensive checklist for sketching the graph of a function by hand without the use of a calculator. It covers essential aspects including the function's domain, intercepts, symmetry, asymptotes, intervals of increase/decrease, local extrema, concavity, and inflection points. While not every item will apply to every function, following these guidelines will help you create a clear and informative sketch. Illustrative examples are included to reinforce the process, demonstrating how to address each checklist item efficiently.

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Section 3.6 – Curve Sketching

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  1. Section 3.6 – Curve Sketching

  2. 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. • Domain • x and y-intercept(s) • Symmetry • Horizontal, Vertical, and Slant Asymptotes • Intervals of Increase or Decrease • Local Maximum and Minimum Values • Concavity and Points of Inflection Once you have completed the checklist, sketch the graph.

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

  4. Answer to Example 1 Even Function.

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

  6. Answer to Example 2 Inflection Points

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

  8. Answer to Example 3 y = x Odd Function.

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

  10. Answer to Example 4 Inflection Points

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

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

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