Math II Day 42 (3-8-10) UNIT QUESTION: How are absolute value equations similar to piecewise functions? Standard: MM2A1 Today’s Question: How do we graph absolute value inequalities? Standard: MM2A1.b,c

Absolute Value Functions General Form: y = a | x – h | + k 1. The graph is V-shaped 2. Vertex of the graph: (h, k) 3.a acts as the slope for the right hand side (the left side is the opposite)

Absolute Value Functions Parent Graph:y = | x | What effect does each one have on the parent graph? y = a | x – h | + k *Opens up/down *Moves left/right *Moves up/down *Fat/skinny

Graphing Abs Value Functions y = |x| + 3 y = |x| -1 y = |x - 2| y = |x + 1| - 3 y = 2 |x| y = ⅔ |x|

1.y = 2 |x - 2| y = 1/3 |x| y = -|x + 5| y = |x| 3.y = -2|x + 2|

Graphing Abs Value Inequalities y < |x| + 3 y ≥ 2 |x| - 5

Characteristics of Functions Domain Range Increasing Decreasing Constant Zeroes Max, Min

Characteristics of Functions Domain Range Increasing Decreasing Constant Zeroes Max, Min

Transformations of Graphs Activity