Absolute Value Functions & Graphs

Parent function

of Abs. Functions

y = |x|

Absolute Value Functions

Spin on linear equations V-shaped graph Has a feel of graphing a linear function. All Absolute Value graphs are in the same

form:

Where b and c will be real numbers.

cbxy

Graphing Absolute Value Functions

Three ways to graph: Use a table Use a TI “Read” the equation.

If you can read a linear eqn., you can read an absolute value eqn.

Using a Table

The table method works for every two-variable equation in the world.

1. Choose an x-value2. Sub in the value for x 3. Simplify4. Your answer is the y-value and now you’ve

found a point on the graph.5. Repeat for 2-4 more x-values and sketch

the function.There’s just one problem…

The Vertex

Abs. Value graphs have two directions. Plot vertex first!!

The vertex for ALL Abs. Value functions is at:

cb,

Example 1Graph 21 xy

)1(

1. Identify b and c b= 1 c= -2

2. Find the vertex x= y = -23. Choose two x-values greater than the x coord. of the vertex and two less than. Lets choose -4,-2, 1, 2.

x |x+1| -2 y -4 |-4 + 1| - 2 1 -2 |-2 + 1| - 2 -1 1 | 1 + 1| - 2 0 2 | 2 + 1| - 2 1

4. Set up a table

Using the TI: Get your Calc!

Make sure the function is solved for y. Hit the ‘y=‘ button Clear out any “old” functions Hit ‘math’ → move over to ‘num’ → hit enter Abs( says “take the absolute value of the

expression in the parenthesis. Enter the expression and close the parenthesis. If there’s a ‘c’, put it in Hit graph and there it is! Hopefully…if not, hit ‘zoom’ and choose zoomfit or zoomstd

Example 2

Go to into ‘y=‘ ‘math’ → move over

to ‘num’ → hit enter Enter the expression

‘x-3’ Close parenthesis!!!!! Then put in +2 Hit Graph Zoom, if needed

23 xyGraph:

“Read the Equation”

The ‘c’ on the outside of the bars moves the parent function up/down. Positive is up, negative is down.

The ‘b’, the constant on the inside of the abs. value bars moves the parent function left/right the OPPOSITE of what you see. Positive goes left and negative goes right.

To flip the V upside-down, there must be a negative number multiplied on the outside of the bars.

Example 3Graph: 25 xy

1. Place Parent Function

2. Move left or right– here we’ll go left to -5

3. Move up or down– here we’ll go down to -2

4. Done