Homework Log Fri 10/2 Lesson 2 – 7 Learning Objective: To graph absolute value functions by transformation Hw: Pg. 111 #16 - 18, 23 – 28, 32, *35, 60, 61

10/2/15 Lesson 2-7 Absolute Value Graphs Day 2 Algebra II

Learning Objective To graph absolute value functions by transformation

1. 𝐲=−𝟐 𝒙 x y -2 -4 -1 -2 V(0 0) 1 -2 2 -4 Vertex: (0, 0) 𝐲=−2 −𝟐 =−𝟒 1. 𝐲=−𝟐 𝒙 𝐲=−𝟐 −𝟏 =−𝟐 𝐲=−2 𝟏 =−𝟐 Vertex: (0, 0) Axis of Sym: x = 0 x y 𝐲=−2 𝟐 =−𝟒 -2 -1 1 2 -4 -2 V(0 0) -2 -4

2. 𝐲= −𝟐𝒙 x y -2 4 -1 2 V(0 0) 1 2 2 4 Vertex: (0, 0) 𝐲= −𝟐(−𝟐) =𝟒 2. 𝐲= −𝟐𝒙 𝐲= −𝟐(−𝟏) =𝟐 𝐲= −𝟐(𝟏) =𝟐 Vertex: (0, 0) Axis of Sym: x = 0 x y 𝐲= −𝟐(𝟐) =𝟒 -2 -1 1 2 4 2 V(0 0) 2 4

3. 𝐲= 𝒙−𝟏 −𝟑 x y -1 -1 -2 V( 1 -3) 2 -2 3 -1 Vertex: (1, -3) 𝐲= −𝟏−𝟏 −𝟑=−𝟏 3. 𝐲= 𝒙−𝟏 −𝟑 𝐲= −𝟏−𝟎 −𝟑=−𝟐 𝐲= 𝟐−𝟏 −𝟑=−𝟐 Vertex: (1, -3) Axis of Sym: x = 1 x y 𝐲= 𝟑−𝟏 −𝟑=−𝟏 -1 2 3 -1 -2 V( 1 -3) -2 -1

Family of Absolute Value Functions

Family of Absolute Value Functions

Family of Absolute Value Functions

Family of Absolute Value Functions

Parent Function: 𝐲= 𝒙 x y -2 2 -1 1 V(0 0) 1 1 2 2 Vertex: (0, 0) Axis of Sym: x = 0 x y -2 -1 1 2 2 1 V(0 0) 1 2

4. Without graphing, identify the vertex, axis of symmetry, and transformation from the parent function 𝐲= 𝒙 𝐲= 𝒙+7 −5 V (-7, -5) Axis of Symmetry: x = -7 Left 7 Down 5

5. Without graphing, identify the vertex, axis of symmetry, and transformation from the parent function 𝐲= 𝒙 𝐲=3 𝒙−2 +1 V (2, 1) Axis of Symmetry: x = 2 Right 2 Up 1 Stretch by factor of 3

6. Without graphing, identify the vertex, axis of symmetry, and transformation from the parent function 𝐲= 𝒙 𝐲= 1 4 𝒙+5 +2 V (-5, 2) Axis of Symmetry: x = -5 Left 5 Up 2 Compress by factor of 1 4

7. Without graphing, identify the vertex, axis of symmetry, and transformation from the parent function 𝐲= 𝒙 𝐲=− 𝒙−8 V (8, 0) Axis of Symmetry: x = 8 Right 8 Reflect over x-axis

8. Without graphing, identify the vertex, axis of symmetry, and transformation from the parent function 𝐲= 𝒙 𝐲= −𝒙 +3 V (0, 3) Axis of Symmetry: x = 0 Up 3 Reflect over y-axis

9. Without graphing, identify the vertex, axis of symmetry, and transformation from the parent function 𝐲= 𝒙 𝐲=7− 𝒙+3 𝐲=− 𝒙+3 +7 V (-3, 7) Axis of Symmetry: x = -3 Left 3 Up 7 Reflect over x-axis

𝐲= −(−𝟐) =2 10. 𝐲= −𝒙 𝐲= −(−𝟏) =1 𝐲= −𝟏 =1 𝐲= −𝟐 =2 x y -2 2 -1 1 Vertex: (0, 0) Axis of Sym: x = 0 x y 𝐲= −𝟐 =2 -2 -1 1 2 2 1 V( 0 0) 1 2

11. 𝐲=− 𝒙+𝟐 +𝟑 x y -4 1 -3 2 V(-2 3) -1 2 1 Vertex: (-2, 3) 𝐲=− −𝟒+𝟐 +𝟑=𝟏 11. 𝐲=− 𝒙+𝟐 +𝟑 𝐲=− −𝟑+𝟐 +𝟑=𝟐 𝐲=− −𝟏+𝟐 +𝟑=𝟐 Vertex: (-2, 3) Axis of Sym: x = -2 x y 𝐲=− 𝟎+𝟐 +𝟑=𝟏 -4 -3 -1 1 2 V(-2 3) 2 1

Ticket Out the Door Without graphing, identify the vertex, axis of symmetry, and transformation from the parent function 𝐲= 𝒙 𝐲=3− −𝒙

Assignment: Pg. 111 #16 - 18, 23 – 28, 32, *35, 60, 61

Warm – up #7 1. Graph 𝐲=−2 𝒙 2. Graph 𝐲= −2𝒙 3. Graph 𝐲= 𝒙−𝟏 −3