Math IIDay 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 FunctionsGeneral 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 FunctionsParent 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| + 3 4. y = 1/3 |x| + 5

2. y = -|x + 5| - 6 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