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ACT Function notation & composition practice questions

Function notation & composition sits in the Functions reporting category on the ACT Math section. Prep36 has 12 questions tagged to this skill, every one with a worked explanation. Three of them are below in full, with the reasoning, so you can see what the skill actually looks like before you practise it.

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What Function notation & composition covers on the ACT

Within this skill the Prep36 bank covers composition of functions, evaluating at a negative input, evaluating a composite at a point, evaluating a quadratic function, evaluating a composite function and evaluating a function at a value.

Math is 45 questions in 50 minutes, which is about 66 seconds each, and it is one of the three sections that average into your composite. The difficulty split across the 12 questions tagged here is 6 easier, 4 medium and 2 harder.

Questions are original, written to the Enhanced ACT format. Prep36 is not affiliated with ACT, Inc.

3 function notation & composition questions, with the reasoning

Question 1 easy

The function f is defined by f(x) = 2x2 - 5x + 1. What is the value of f(-2) ?

  1. A. -1
  2. B. 3
  3. C. 11
  4. D. 19 correct
Why: Substituting gives 2(-2)2 - 5(-2) + 1 = 2(4) + 10 + 1 = 19. The choice -1 comes from subtracting 10 rather than adding it, forgetting that -5 times -2 is positive, which yields 8 - 10 + 1. The choice 3 comes from treating (-2)2 as -4, which yields -8 + 10 + 1. The choice 11 likewise comes from a sign slip in the middle term rather than a complete evaluation. Tip: wrap every substituted negative in parentheses before evaluating so the squaring applies to the sign as well as the digit.
Question 2 medium

The functions f and g are defined by f(x) = 2x − 5 and g(x) = x² + 1. What is the value of f(g(3))?

  1. A. 2
  2. B. 10
  3. C. 15 correct
  4. D. 20
Why: Composition works inside out. First g(3) = 3² + 1 = 10, then f(10) = 2(10) − 5 = 15. Choice A (2) reverses the order and computes g(f(3)) = g(1) = 2, choice D (20) applies f but drops the −5, and choice B (10) stops after the inner function. Tip: f(g(3)) means g goes first, always. Compute the inner value, write it down as a single number, then feed that number into the outer function.
Question 3 hard

If f(x) = 2x + 1 and g(x) = x², what is the value of f(g(3))?

  1. A. 19 correct
  2. B. 37
  3. C. 49
  4. D. 13
Why: Work from the inside out: g(3) = 3² = 9, then f(9) = 2(9) + 1 = 19. The distractors reverse or garble the order: 49 computes g(f(3)) = (2 · 3 + 1)² instead, 13 uses g(3) = 6 by squaring incorrectly as 2 · 3, and 37 doubles 18 before adding 1 in the wrong place. Tip: in a composition f(g(x)), evaluate the inner function g first, then feed its output into f. The order is not interchangeable.

The explanation is the point. Getting a question wrong tells you nothing you did not already suspect; knowing which step you missed is what changes the next one.

Practise the rest of the 12

The other 9 questions on this skill are in the free question bank, filterable by difficulty, each with the same worked explanation. No account and no card.

Open the Math bank

Frequently asked questions

How many ACT function notation & composition questions does Prep36 have?
12, each tagged to this skill and each with a worked explanation.
Are these real ACT questions?
No. They are original questions written to the Enhanced ACT format. Prep36 is not affiliated with ACT, Inc.
Is the Math section part of the composite?
Yes. On the Enhanced ACT the composite is the average of English, Math and Reading. Science is optional and reported separately.
Keep readingACT Math practiceEvery Math skill in one place.How many questions can you miss?The miss budget for every score.ACT Score CalculatorTurn raw scores into a composite.
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