ABSOLUTE VALUE FUNCTION

Absolute Value:

A real number (rational and irrational numbers) can be represented by a position on the number line.  Absolute values will be the distance from the origin (zero) to the numbers.

Example 1:

x = |3|

Go 3 units to the left and 3 units to the right from the origin in the number line.

x = - 3

x =  3

• Close dots in the number line indicate that end points are included.

• Open dots in the number line indicate that end points are not included.

Example 2:

| x – 5 | = 2

(x – 5) will go 2 units to the left and 2 units to the right from the origin.

Example 3:

| x – 4 | > 7

(x – 4) will go more than 7 units to the left and more than 7 units to the right from the origin.

 Example 4:

Graph f(x) = |x|,  x € R

First graph f(x) = x

Then reflect the portion of the graph below the x-axis in the x-axis as illustrated below:

Example 5:

Graph y = |x² - 3x - 28|

First graph y = x² - 3x - 28

Then reflect the portion of the graph below the x-axis in the x-axis as illustrated below:

Example 6:

 Plot   |2x⁴ – x³ - 47x² + x + 45|

First graph y = 2x⁴ – x³ - 47x² + x + 45

Then reflect the portion of the graph below the x-axis in the x-axis as illustrated below: