Precalculus Assignment

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Math 30-1: Unit 1 Functions and Operations Assignment

Name: _____________________________ /18 Marks

If your name does not appear in your writing on the hardcopy scan – you will lose one mark!

1. Given 𝑓(𝑥) = 3𝑥2 + 2, 𝑔(𝑥) = 4𝑥, and ℎ(𝑥) = 7𝑥 − 1, determine each of the following

combined functions. Fully simplify all final equations.

a. 𝑦 = 𝑓(𝑥) + 𝑔(𝑥) − ℎ(𝑥) b. 𝑦 = 𝑔(𝑥)ℎ(𝑥)

𝑓(𝑥)

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2. Given 𝑓(𝑥) = √𝑥 − 1 and 𝑔(𝑥) = 𝑥 − 2, determine the following:

a. the domain of 𝑓(𝑥) and the domain of 𝑔(𝑥)

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b. Explain why the domain of 𝑓(𝑥) ∙ 𝑔(𝑥) is the same as the domain of 𝑓(𝑥) and not the

same as 𝑔(𝑥).

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3. Let ℎ(𝑥) = 𝑓(𝑥)𝑔(𝑥). If 𝑓(𝑥) = 2𝑥 + 5 and ℎ(𝑥) = −2𝑥2 − 5𝑥, determine 𝑔(𝑥).

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4. Consider the following graphs of 𝑓(𝑥) and 𝑔(𝑥).

Determine which graph (A, B, or C shown below) matches each of the following

combined functions of 𝑓(𝑥) and 𝑔(𝑥).

𝑦 = 𝑓(𝑥) − 𝑔(𝑥) Graph: _____

𝑦 = 𝑔(𝑥) − 𝑓(𝑥) Graph: _____ /2

𝑦 = 𝑓(𝑥) + 𝑔(𝑥) Graph: _____

5. Use the graphs of 𝑓(𝑥) and 𝑔(𝑥) to evaluate the following:

a. (𝑓 ∙ 𝑔)(−2) /1

b. ( 𝑓

𝑔 ) (1) /1

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6. Use the graphs of 𝑓(𝑥) and 𝑔(𝑥) to evaluate the following.

a. 𝑓(𝑔(−4)) /1

b. 𝑔(𝑓(−3)) /1

7. If 𝑓(𝑥) = 3𝑥 + 4 and 𝑔(𝑥) = 𝑥2 − 1, determine each of the following.

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a. 𝑓(𝑔(𝑥)) b. 𝑓(𝑓(𝑥))

c. 𝑔(𝑓(−2)) d. 𝑔(𝑔(3))

8. Given 𝑓(𝑥) = √𝑥 and 𝑔(𝑥) = 𝑥 − 3, determine the domain and range of:

a. 𝑦 = 𝑓(𝑔(𝑥)) /1 b. 𝑦 = 𝑔(𝑓(𝑥)) /1