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))

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

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.

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.

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

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.

Example 1.A. Graph g(x) = |x| + 3. 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.

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.

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.

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.

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)

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))

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

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.

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