describe the transformations. 1. 2. graph the function. 3. 4
TRANSCRIPT
Describe the transformations.
1. 2. Graph the Function.
3. 4.
Warm Up
34)( xxf
42)( xxf
32
1)( xxg
24)( xxg
1. Subtract under the radical
2. Add under the radical
3. Multiply under the radical
4. Divide under the radical
5. Add outside of the radical
6. Subtract outside of the radical
a) Move upb) Move right
c) Move downd) Move lefte) Stretchf) Compress
Recap Radical Shifts Matching
23 xy
We simplify the radicand if possible
Check the 1st and 3rd lines in your calculator.
Do they match?
Parent Function:
Graphing a Cubed Root Function
3 x
x y
0
1
2
4
9
How do Cubed Roots Move?
Subtract under the radical
Add under the radical
Multiply under the radical
Divide under the radical
Add outside of the radical
Subtract outside of the radical
Cubed Root Transformations
Absolute Value and Step Functions
October 8th
By definition, absolute value is the distance from zero.
Can we ever have a negative distance?
How far away from zero is 3? How about -2?
Absolute Value
How many ways are there to be 4 units away from zero?
Absolute value
Evaluating an absolute value expression still requires PEMDAS. We treat absolute value bars like parenthesis, so we want to simplify inside of the bars first.
Example: Evaluate when x = 1.
Evaluating absolute value
Examples:
Graphing absolute value functions
Why do you think the graph looks like this?
Domain:
Range:
Domain and Range
This will always give us the basic shape of our absolute value functions.
Graphing absolute value functions
We will use what we know about transformations to shift the graph.
Based on what happened to radicals, describe the transformations that might occur for each of the following from the parent function:
Check this in your calculator.
Add/Subtract INSIDE the bars: ◦ opposite direction, left and right
Multiply by a value greater than 1 in FRONT: ◦ stretch (skinny), slope of right side
Multiply by a value between 0 and 1 in FRONT: ◦ wider, slope of right side
Add/Subtract after the bars: ◦ up and down
How Absolute Value Functions Move
To graph absolute value functions with transformations, we want to look from left to right. We will graph the transformations in that order.
Graphing with transformations:
Domain:
Range:
Domain: Range:
Examples:
Domain: Range:
You Try – sketch the graphs of each of the following and give their domain and range:
We are looking for groups of 3◦Graph◦Function◦Description of Transformations
Matching Activity – Partner Race
Worksheet
Homework