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Sign Diagrams

Sign diagrams are a tool for capturing the critical information about a function.  Namely, it answers the question, "What's your sign;-)"  [Note: I am not condoning the use of horoscopes, but the pun is too good to resist.]

For information in the text: Precalculus, Functions and Graphs 5th ed. by Barnett, Ziegler, and Byleen, look in section 1.8 beginning on page 82 for an introduction.

Contents.

  1. Overview.
  2. How to Construct a Sign Diagram.
  3. Example: Quadratic Function.
  4. Example: Rational Function (asymptote).
  5. Example: Rational Function (asymptote and hole).
  6. Example: Square Root Function (undefined region).
  7. Handout: Construct Sign Diagrams from a Graph.
  8. Handout: Use a Sign Diagram to Find the Domain.

Overview.

The word "sign" in sign diagram refers to the y value on a graph.  There are only 4 possible signs that  y value can take on:

  1. Positive: "+"
  2. Negative: "-"
  3. Zero: "0"
  4. Undefined: "*"

Furthermore, there are three types of undefined on sign diagrams:

  1. Vertical Asymptotes (most commonly seen).
  2. Holes.
  3. Undefined Regions.

 

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  last modified December 16, 2010