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Absolute value plays an important role with distance between points on a coordinate line and with algebraic calculations with radicals. You should know how to break an absolute value equation into its equivalent piecewise equations. Inequalities can be used to express information about a range of numbers on a coordinate line.

Definition of  :  f(x)= in a piecewise function notation is

The graph of this function in the standard (zoom 6. Standard) window looks like:

Note the graph associated with this absolute value is a set of 2 lines (or rays) which meet at a point.

Use the graphing calculator and look at the graph of . Draw a picture of the graph of this equation using the grid at the left. Set your window to Zoom 4. Decimal.

What does this tell you about  ? 

So another way to look at would be in a piecewise function:

.

What does this say to you?

Often an absolute value is written in an inequality statement.  To solve an absolute value within an inequality you will need to first rewrite the inequality statement without the absolute value.  Here are two examples:

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Check Your Understanding: (Remember to write down your answers.)
 

Solve and represent the solutions to these inequalities on a number line:

1. 

2. 

3. 

4. 

This page was last modified on 01/06/07

© Rahn, 2000