6th Grade Math Textbook, Fundamentals

 &KDSWHU

Enrichment:

Graphing with Absolute Values

Objective To make a table of integer values of xfor graphing absolute-value functions
and to describe how the graphs change as the functions vary

You have found absolute values of numbers and simplified absolute value
expressions. Now you will extend your understanding of absolute value to
graph absolute-value functions.

The graphs of absolute-value functions are all related to the graph of the

absolute-value function: f(x) |x|. The f(x) notation is another way to

represent the y-values of x.

To graph f(x) |x|, first make a table of values.

You may use the values in the table below or

choose others.

Plot the values from your table. Use the f(x) values as the

y-coordinates. Then connect the points. The graph below uses

the table of values above.

Because |x| is always greater than or equal to zero for all values of x,

there are no points in Quadrant III or IV. Notice that the part of the

graph in Quadrant II is the reflection image of the part of the graph

in Quadrant I. This is because |x| |x| for any number x. That is,

the absolute value of a number is the same as the absolute value of

its opposite.

f(x) |x|

Input

x

Output

f(x)

4 |4|  4

2 |2|  2

0 |0|  0

2|2|  2

4|4|  4

y

x

4XDGUDQWII 4XDGUDQWI

4XDGUDQWIII 4XDGUDQWIV

f(x)  |x|