Parent Functions & Transformations Absolute Value Functions [PDF]

Algebra II Absolute Value Functions 𝒚 = |𝒙|

Quadratic Functions 𝒚 = 𝒙𝟐

Unit 1 Notes: Parent Functions & Transformations

1. 𝑦 = |𝑥 − 3| + 2

2. 𝑦 = 3|𝑥 + 3| − 2

3. 𝑦 = −|𝑥 − 2| − 1

4. 𝑦 = − 3 |𝑥 − 2| + 1

5. 𝑦 = (𝑥 − 4)2 − 3

6. 𝑦 = (𝑥 + 2)2 + 1

7. 𝑦 = −(𝑥 + 1)2 + 3

8. 𝑦 = −(𝑥 − 2)2 − 1

2

Square Root Functions 𝒚 = √𝒙

Cube Functions 𝒚 = 𝒙𝟑

9. 𝑦 = √𝑥 − 5 + 1

10. 𝑦 = √𝑥 + 3

11. 𝑦 = √𝑥 + 3

12. 𝑦 = −√𝑥 + 2 − 4

13. 𝑦 = 𝑥 3 − 2

14. 𝑦 = −(𝑥 − 1)3 + 4

15. 𝑦 = (𝑥 + 2)3 − 4

16. 𝑦 = −(𝑥 − 2)3

Cube Root Functions

3

𝟑

𝒚 = √𝒙

17. 𝑦 = √𝑥 − 2 + 3

3

18. 𝑦 = √𝑥 + 4 − 1

Match each function to the correct graph. 1. 2. 3. 4. 5. 6. 7. 8. A)

B)

E)

F)

C)

G)

D)

H)

Domain & Range Practice 1.

2.

3.

Domain: __________________

Domain: __________________

Domain: __________________

Range:____________________

Range:____________________

Range:____________________

Multiple Choice: Choose the best answer for each question. 4. What is the domain of f ( x) = A. B. C. D.

[0, ∞) [2, ∞) [3, ∞) (-∞, ∞)

5. What is the range of f ( x) = A. B. C. D.

x−3 +2?

x−3 +2?

[0, ∞) [2, ∞) [3, ∞) (-∞, ∞)

6. The domain and range of __?__ is all real numbers. A. y = (x – 1)2 – 6 B. y = 2x + 5 C. y = 3x – 7 D.

y = x+4

7. Which rational function’s domain excludes −3 ? A.

1 x+3

B. y =

1 x−3

3 x

D. y =

−3 x

C. y =