Absolute Value Functions & GraphsPresentation Transcript
Absolute Value Functions & Graphs Parent function of Abs. Functions y = |x|
Absolute Value Functions
Spin on linear equations
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.
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.
Choose an x-value
Sub in the value for x
Your answer is the y-value and now you’ve found a point on the graph.
Repeat for 2-4 more x-values and sketch the function.
There’s just one problem…
Abs. Value graphs have two directions.
Plot vertex first!!
The vertex for ALL Abs. Value functions is at:
1. Identify b and c b= 1 c= -2 2. Find the vertex x= y = -2 3. 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
Go to into ‘y=‘
‘ math’ -> move over to ‘num’ -> hit enter
Enter the expression ‘x-3’
Then put in +2
Zoom, if needed
“ 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.