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How to Construct a Sign Diagram.

What follows is a method that will work many times.  However, memorization should never be considered of more importance than understanding.

Method:

1. Find all critical points.  This is often done by factoring and/or by understanding the function.
2. Draw a number line.
3. Place all of the critical points on the number line.  Label the points with their x values below the point.
4. Above the point, draw an arrow down to the point and include a description of the point above the arrow.  That is, is it a zero, vertical asymptote, or a hole.
5. Classify the regions in between each critical point as positive, negative, or undefined.

Note: it may be helpful to use solid points for zeros and open points for asymptotes and holes.

Examples:

What follows are two completed sign diagrams.

Example 1:
Example 2:

  last modified December 16, 2010