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Functions — SHSAT practice questions

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What this topic is

Functions on the SHSAT Mathematics section covers evaluating a rule at a given input, composing one function with another, finding an unknown coefficient from a known output, and using a functional identity that relates values at shifted inputs.

A student has to substitute carefully, keep composition in the correct order, and apply a relation repeatedly to reach a later argument. Questions usually ask for one numerical result, such as a composed value, the constant k, or F at a later input.

Common traps are reversing composition, plugging in the wrong number, and arithmetic slips when iterating a rule like F of x plus two. Answer choices are typically integers.

Sample questions

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Question 1Mid

Functions f(x)=x+2f(x)=x+2 and g(x)=3x−1g(x)=3x-1 are defined for all real numbers. What is f(g(3))f(g(3))?

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Answer: B — 10

Composition is evaluated inside out. First find g(3)=8g(3)=8, and then apply ff to get 10.

Question 2Easier

For p(x)=kx−3p(x)=kx-3, it is known that p(4)=9p(4)=9. What is the value of kk?

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Answer: B — 3

The function value creates a linear equation in kk; isolating the parameter gives 3.

Question 3Mid

A function satisfies F(x+2)=3F(x)−2F(x+2)=3F(x)-2 for every allowed xx. If F(1)=4F(1)=4, what is F(5)F(5)?

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Answer: C — 28

The input increases by 2 each time, so two applications are needed. They produce 10, then 28.

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Practice 91 Functions questions in the app

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