Absolute Value Functions & Graphs Parent function of Abs. Functions y = |x|
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