2.1 Graphing Absolute Value Functions Notes - page 49
Essential Question: How can you identify the key features of the graph of an absolute
value function?
Recall that an EVEN function is defined as 𝑓(−𝑥) = 𝑓(𝑥) and has reflective symmetry
over the y-axis.
𝑓(𝑥) = |𝑥|
I. Transformations of Absolute Value Functions
Use information from lesson 1.3 to help determine what the transformations to
the graph will be. Identify the vertex of the absolute value function.
1. 𝑔(𝑥) = 4|𝑥 − 5| − 2
1
3. 𝑔(𝑥) = − 5 |𝑥 + 6| + 4
1
2. 𝑔(𝑥) = |− 2 (𝑥 + 3)| + 1
7
4. 𝑔(𝑥) = 3 |𝑥 − 7|
II. Graphing Absolute Value Functions with vertex (h, k) – page 50
You can apply general transformations to absolute value functions by changing
parameters in the equation 𝑔(𝑥) = 𝑎|𝑏(𝑥 − ℎ)| + 𝑘.
Example 1: Given the function 𝑔(𝑥) = 𝑎|𝑏(𝑥 − ℎ)| + 𝑘, find the vertex of the function.
Use the vertex and at least two other points to help you graph g(x).
III. Writing Absolute Value Functions – page 51
Example 2: Given the graph of an absolute value function, write the function in the form
𝑔(𝑥) = 𝑎|𝑏(𝑥 − ℎ)| + 𝑘.
IV. Modeling with Absolute Value Functions – page 52-53
Topic:
Setting up the Problem:
Analyze Information:
Formulate a Plan:
Solve:
Justify and Evaluate: