1. 2.7 Absolute Value Functions and Transformations Parent Function of Absolute Value  F(x)= I x I  Graph is a “v-shape”  2 rays meeting at a vertex V(0,0) Y=x when x > 0 (m=1, b=0) Y = -x when x < 0 (m=-1, b=0)

2. Transformations: changes Rigid Transformations – Keep the same shape and size (just new location) 1. Translations (slides or shifts) Horizontal (opposite direction of what you think) Vertical 2. Reflections (flips) Over x-axis Over y-axis Non-rigid Transformations – New shape is distorted from original 1. Vertical stretches- pull away from x-axis (skinny) 2. Vertical shrinks –push towards x-axis (fat)

3. Transforming Y= a I x – h I + k with vertex V(h,k): Correct order 1. Horizontal shifts (translations) – Add “inside” symbol: slide left – Subtract “inside” symbol: slide right 2. Reflect over y-axis (flip y) – Negative before x “inside” symbol 3. Reflect over x-axis (flip x) – Negative in front of whole function 4. Vertical stretch or shrink – Multiply by a number out front I a I > 1 = stretch (skinny) 0 < I a I < 1 = shrink (fat) 5. Vertical shifts (translation) – Add “outside” symbol: slide up – Subtract “outside” symbol: slide down

4. Examples: Graph & compare with y= I x I 1. y = I x + 4 I – 2 2. y = I x – 2 I + 5 3. y = I x – 3 I – 1

5. More examples: Graph and compare to y= I x I 4. y = ½ I x I 5. y = -3 I x I 6. y = 2 I x I 7. y = - ¼ I x I

6. More examples: Graph and compare to y = I x I 8. y = -2 I x – 1 I + 3 9. y = -3 I x + 1 I – 2 10. y = -4 I x + 3 I + 1

7. Given y=f(x), compare transformations to the parent f(x) and graph. 11. y= -f(x – 2) – 5 12. y= 2 f(x + 3)- 1 13. y = -2f(x)