Graph f(x) = −𝑥 if 𝑥<−1 0 if −1≤𝑥≤ 1 𝑥 if 𝑥>1 Find f(1). Problem of the Day

Section 2-6, 2-7, & 2-8 Absolute Value Functions and Inequalities / Transformations

Then Now Objectives You graphed piecewise functions. Write and graph absolute value functions. Describe transformations of functions. Graph absolute value inequalities.

Common Core State Standards Content Standards Common Core State Standards F.IF.7.b – Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. F.BF.3 – Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative). A.CED.3 – Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. Mathematical Practices 1) Make sense of problems and persevere in solving them. 6) Attend to precision.

Absolute Value Function: a function that contains an algebraic expression within absolute value symbols. Vocabulary

Parent Function of Absolute Value Functions

Example 4 (2-6) and Examples 2, 3, and 4 (2-7) Graph the function: f(x) = |x – 2|. Describe the transformation. Example 4 (2-6) and Examples 2, 3, and 4 (2-7)

Example 4 (2-6) and Examples 2, 3, and 4 (2-7) Graph the function: f(x) = -|x| + 1. Describe the transformation. Example 4 (2-6) and Examples 2, 3, and 4 (2-7)

Example 4 (2-6) and Examples 2, 3, and 4 (2-7) Graph the function: f(x) = |x| + 1. Describe the transformation. Example 4 (2-6) and Examples 2, 3, and 4 (2-7)

Graph: y ≤ 2|x| + 3 Example 3 (2-8)

Graph: y > 3|x + 1| Example 3 (2-8)

Graph: y ≥ |x| – 2 Example 3 (2-8)

Transformations of Functions

p. 114 #15, 19, 23, 24, 28, 29 (Describe the transformation p.114 #15, 19, 23, 24, 28, 29 (Describe the transformation. Do NOT graph.) AND p.114 #36, 38 p.119 #23, 24 (Graph) Homework

If the graph is translated 4 units up and 2 units right, what is the new equation of the function? If the graph is translated 5 units down and 3 units right, what is the new equation of the function? If the graph is translated 3 units up and 7 units left, what is the new equation of the function? If the graph is translated 3 units down and 6 units left, what is the new equation of the function? Problem of the Day

Second Problem of the Day! Graph 𝑓 𝑥 >3 𝑥−2 −3 Second Problem of the Day!