1. Daily Warm Up Graph the following functions by making a table. x
f(x) =| x|
f(x)
(x, f(x)) x
f(x) =| x + 3 | - 5
f(x)
(x, f(x))

2. Graphing Absolute Value Functions Notes 3.7
Goals:
Translate graphs of absolute value functions
Stretch, shrink, & reflect graphs of absolute value functions
Combine transformations of absolute value functions

3. Recall Core Vocabulary
Family of Functions—
a group of functions with similar characteristics
Parent Function
the most basic function in a family of functions
Linear Parent Function
f(x) = x
Use popsicle sticks to quiz students on these vocabulary words. If the students cannot remember have them rewrite the definitions.

4. Recall Core Vocabulary
Transformation— changes the size, shape, position, or orientation of a graph.
Types of Transformations
Translation—Shifts up or down
Reflection—Over x or y-axis
Horizontal Shrink or Stretch
Vertical Shrink or Stretch
Use popsicle sticks to quiz students on these vocabulary words. If the students cannot remember have them rewrite the definitions.

5. Absolute Value Function
Core Concept
Absolute Value Function
Characteristics:
A function that contains an absolute value expression
Parent function: f(x) = |x|
V-Shaped Graph
Vertex is where the graph changes direction

6. Recall Daily Warm Up Graph the following functions g(x) = |x + 3| – 5
What are the transformations from
f(x) = |x| to g(x) = |x + 3| – 5?
Have students describe the transformations.

7. Example 1.A.
Graph g(x) = |x| Describe the transformations from the parent function to the graph of g. State Domain & Range. x
f(x) =| x|
f(x)
(x, f(x))
Have students describe the transformations.

8. Example 1.B.
Graph m(x) = |x – 2|. Describe the transformations from the parent function to the graph of m. State Domain & Range. x
f(x) =| x|
f(x)
(x, f(x))
Have students describe the transformations.

9. Example 2.A.
Graph q(x) = 2|x|. Describe the transformations from the parent function to the graph of q. State Domain & Range. x
f(x) =| x|
f(x)
(x, f(x))
Have students describe the transformations.

10. Example 2.B.
Graph q(x) = |x|. Describe the transformations from the parent function to the graph of q. State Domain & Range. x
f(x) =| x|
f(x)
(x, f(x))
Have students describe the transformations.

11. An absolute value function written in the form
Core Concept
Vertex Form
An absolute value function written in the form
g(x) = a|x – h| + k
Vertex: (h,k)
examples:
h(x) = –3|x – 2|
with vertex: (2,0)
p(x) = |x|+5
with vertex: (0,5)
q(x) = 4|x+3|–9
with vertex: (–3,–9)

12. Example 3.
Graph f(x) = |x + 2| – 3 and g(x) = |2x + 2| – 3. Compare the graph of g to the graph of f. x
f(x) =| x|
f(x)
(x, f(x))
Fill in tables with students (use popsicle sticks)
Have students describe the transformations. x
f(x) =| x|
f(x)
(x, f(x))

13. Combining Transformations
Recall Core Concept
Combining Transformations
Step 1: Translate the graph horizontally h units .
Step 2: Use “a” to stretch or shrink the resulting graph from step 1. .
Step 3: Reflect the graph from step 2 when a<0 (when a is negative) .
Step 4: Translate the graph from step 3 vertically k units

14. Example 4
Let g(x) = –2|x – 1| + 3. Describe the transformations from the parent function. Graph g. x
f(x) =| x|
f(x)
(x, f(x))
Have students describe the transformations.

15. Practice Extra Practice – In Class Worksheet Hw day 1– Big Ideas TB
Pg. 160 #1-3, 5-25 odd,
Hw day 2– Big Ideas TB
Pg. 160 #6, 8, 10, 24, 30, 32, 36, 38, 41, 42