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Domain and Range of Radical Functions

Sketch the graph of each function.

Identify the domain and range of each function.

3) 𝑦 = √𝑥 + 2 − 3

4) 𝑦 = √𝑥 − 13

− 1

5) 𝑦 = √𝑥 − 2 + 5

6) 𝑦 = √(𝑥 + 1)3 − 4

7) 𝑦 = 3√3𝑥 + 6 + 5

8) 𝑦 = √(2𝑥 − 1)3 − 4

9) 𝑦 = 6√3𝑥2 + 6 + 5

10) 𝑦 = √(2𝑥2 − 2)3

− 4

11) 𝑦 = 4√4𝑥3 + 32 − 1

12) 𝑦 = √(4𝑥 + 8)3 − 2𝑥

13) 𝑦 = 7√−2(2𝑥 + 4) + 1

14) 𝑦 = √(4𝑥2 − 5)5

− 2

15) 𝑦 = 2𝑥√5𝑥4 + 6 − 2𝑥

16) 𝑦 = 6√(8𝑥6 + 2𝑥 + 8)3

− 2

1) y = √𝑥 + 8

2) y = 2√𝑥 − 4

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Date: ___________

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Answers

Domain and range of radical functions

3) domain: 𝑥 ≥ −2

range: 𝑦 ≥ −3

4) domain: {all real numbers}

range: {all real numbers}

5) domain: 𝑥 ≥ 2

range: 𝑦 ≥ 5

6) domain: {all real numbers}

range: {all real numbers}

7) domain: 𝑥 ≥ −2

range: 𝑦 ≥ 5

8) domain: {all real numbers}

range: {all real numbers}

9) domain: {all real numbers}

range: {all real numbers}

10) domain: {all real numbers}

range: {all real numbers}

11) domain: 𝑥 ≥ −2

range: 𝑦 ≥ −1

12) domain: {all real numbers}

range: {all real numbers}

13) domain: 𝑥 ≤ −2

range: 𝑦 ≥ 1

14) domain: {all real numbers}

range: {all real numbers}

15) domain: {all real numbers}

range: {all real numbers}

16) domain: {all real numbers}

range: {all real numbers}

1)

2)