Functions — SHSAT practice questions

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Practice 91 Functions questions in the app

What this topic is

A function assigns exactly one output to each input, and f(x) notation names that rule.

Many questions on functions ask for a value, such as f evaluated at a number, which means substituting that number for x everywhere it appears. Composition is a frequent twist: in f(g(x)), the inner function g is applied first and its output becomes the input of f, and working in the wrong order gives a different answer.

Other items give one known output and ask for a missing coefficient, or define a function by a rule that links one value to the next, which must be applied step by step.

Sample questions

Pick an answer to see whether it is right — nothing is saved, and nothing needs an account.

Question 1Mid

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

8✗ Not this one10✓ Correct13✗ Not this one14✗ Not this one

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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 2Easier

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

2✗ Not this one3✓ Correct4✗ Not this one12✗ Not this one

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Answer: B — 3

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

Question 3Mid

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

8✗ Not this one10✗ Not this one28✓ Correct82✗ Not this one

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Answer: C — 28

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

Every question is picked for where you are right now, wrong answers come back until they stick, and it all works offline.

Practice 91 Functions questions in the app

Functions — SHSAT practice questions

What this topic is

Sample questions

More SHSAT topics

Mathematics