Functions — SHSAT practice questions

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.

Section: Mathematics 57 questions on the paper
91 practice questions in the app

Sample questions

Question 1

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

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Answer: B — 10

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

Question 2

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

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Answer: B — 3

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

Question 3

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

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Answer: C — 28

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

Practice 91 Functions questions in the app

Functions — SHSAT practice questions

Sample questions

More SHSAT topics

Mathematics