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