If f(x) = 3x^2 - 2x + 1, what is f(-2)?

C. 17. Substitute with parentheses: f(-2) = 3(-2)^2 - 2(-2) + 1. Simplify each term: 3(4) = 12 and -2(-2) = 4. Add: 12 + 4 + 1 = 17.

The function h is defined by h(x) = a × b^x, where a and b are positive constants. If h(1) = 6 and h(3) = 54, what is h(0)?

B. 2. Divide the outputs: (h(3))/(h(1)) = (ab^3)/(ab) = b^2 = (54)/(6) = 9, so b = 3. Use h(1) = ab = 6: a = (6)/(3) = 2. Then h(0) = a × b^0 = 2 × 1 = 2.

ACT Math reporting category

ACT Functions Practice

Functions is the ACT math reporting category about rules that pair each input with exactly one output: notation, evaluating, graphs, transformations, and features of linear, quadratic, exponential, and trigonometric functions. According to ACT, it makes up 17–20% of scored math questions, within Preparing for Higher Math.

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17–20% of scored Math questions3 original questionsInstant answer checks

At a glance

Functions on the ACT: the key numbers

Section and category facts from ACT.org, checked October 9, 2026. Time per question is ACT's section time divided by its question count.
Section	ACT Math: 45 questions in 50 minutes
Scored questions	41 scored, 4 field test
Reporting category	Functions (part of Preparing for Higher Math)
Share of scored questions	17–20%, according to ACT
Average time per question	About 67 seconds
Counts toward the Composite	Yes
Practice on this page	3 original questions: Easy, Medium, Hard

What this tests

What does ACT Functions test?

Function notation. Read and use $f (x)$ notation, evaluate a function at a given input, and find the input that gives a stated output.
Composition of functions. Evaluate expressions such as $f (g (x))$ by working from the inside out.
Graphs and key features. Identify intercepts, maximum and minimum values, domain, range, and where a function increases or decreases, from a graph or an equation.
Graph transformations. Describe how shifts, stretches, and reflections change an equation and its graph, such as moving from $y = x^{2}$ to $y = (x - 3)^{2} + 1$ .
Function families. Compare linear, quadratic, exponential, and trigonometric functions using features such as slope, vertex, growth factor, period, and amplitude.

Practice questions

Practice ACT Functions questions

Pick an answer to check it. Each question has one correct choice.

Question 1 of 3Easy

f (x) = 3 x^{2} - 2 x + 1

, what is

f (- 2)

Show answer and explanation

Correct answerC. $17$

How to solve it

Substitute with parentheses: $f (- 2) = 3 (- 2)^{2} - 2 (- 2) + 1$ .
Simplify each term: $3 (4) = 12$ and $- 2 (- 2) = 4$ .
Add: $12 + 4 + 1 = 17$ .

Why the other choices miss

- 7

squares

- 2

- 4

9

treats

- 2 (- 2)

- 4

instead of

4

41

multiplies before squaring, computing

(3 (- 2))^{2} = 36

instead of

3 (- 2)^{2} = 12

Question 2 of 3Medium

Let

f (x) = 2 x + 1

and

g (x) = x^{2} - 3 x

. What is the value of

f (g (- 1))

Show answer and explanation

Correct answerD. $9$

How to solve it

Start inside: $g (- 1) = (- 1)^{2} - 3 (- 1) = 1 + 3 = 4$ .
Use that output as the input to $f$ : $f (4) = 2 (4) + 1 = 9$ .

Why the other choices miss

- 4

multiplies

f (- 1) = - 1

g (- 1) = 4

instead of composing.

- 3

comes from a sign slip,

g (- 1) = 1 - 3 = - 2

, followed by

f (- 2) = - 3

4

g (- 1)

, which stops after the inside step and never applies

f

Question 3 of 3Hard

The function

h

is defined by

h (x) = a \cdot b^{x}

, where

a

and

b

are positive constants. If

h (1) = 6

and

h (3) = 54

, what is

h (0)

Show answer and explanation

Correct answerB. $2$

How to solve it

Divide the outputs: $\frac{h ( 3 )}{h ( 1 )} = \frac{a b ^{3}}{ab} = b^{2} = \frac{54}{6} = 9$ , so $b = 3$ .
Use $h (1) = ab = 6$ : $a = \frac{6}{3} = 2$ .
Then $h (0) = a \cdot b^{0} = 2 \cdot 1 = 2$ .

Why the other choices miss

- 18

treats the function as linear, using a slope of 24 and stepping back one unit from

h (1) = 6

3

is the base

b

, not

h (0)

18

multiplies

h (1)

by 3 to step backward instead of dividing by 3.

Avoid these traps

What mistakes do students make on Functions?

Squaring negatives without parentheses

Evaluating $3 x^{2}$ at $x = - 2$ by writing $- 2^{2}$ gives $- 4$ instead of $4$ , which changes the sign of the whole term.

Fix: Substitute with parentheses every time, as in $3 (- 2)^{2}$ .

Composing in the wrong order

For $f (g (x))$ , students apply $f$ first because it is written first.

Fix: Work from the inside out: evaluate $g$ first, then use that output as the input to $f$ .

Treating exponential functions as linear

Given two points on an exponential function, students find a slope and extend a line through them, which gives the wrong values.

Fix: Divide the outputs to find the growth factor, then multiply to move forward or divide to move backward.

Study method

How should you practice ACT Functions?

Say each function in words before you start, for example " $g$ squares the input, then subtracts three times the input. "
Substitute with parentheses around every input, especially negative numbers and fractions.
For compositions, write the inside result on its own line before using it.
Sketch a quick graph or a table of values when a question asks about features like intercepts or maximum values.
Practice mixed function sets in Dolphin, and redo each missed question a few days later without looking at the solution.

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FAQ

Questions about ACT Functions

What does the ACT Functions category cover?

It covers function definitions and notation, evaluating and composing functions, reading graphs, transformations, and the features of linear, quadratic, exponential, and trigonometric functions. The questions on this page practice evaluating a quadratic, composing two functions, and finding an exponential function from two points.

What share of ACT math is Functions?

According to ACT, Functions makes up 17–20% of scored math questions. ACT groups it with Number & Quantity, Algebra, Geometry, and Statistics & Probability under Preparing for Higher Math, which makes up 80% of scored math questions.

Do I need trigonometry to practice ACT Functions?

Trigonometric functions are one of the function families in this category, so it helps to know the sine and cosine graphs, period, and amplitude. If time is short, make sure linear, quadratic, and exponential functions are solid first, then add trigonometric features.

How should I review a missed Functions question?

Find the exact step that went wrong: substitution, order of operations, composition order, or mixing up function families. Rewrite that step correctly, then solve a similar question from scratch. Reviewing the step, not only the final answer, makes the same error easier to catch next time.

Is there a penalty for wrong answers on ACT math?

No. ACT does not penalize incorrect answers, so answer every question. If a Functions question is taking too long, eliminate what you can, choose an answer, and come back to it if time allows.

Related practice

Sources

Where these facts come from

ACT: Understanding Your ACT Scores: reporting categories, category shares, Composite calculation, and scoring.
ACT: Test Enhancements and Changes: section length, question counts, and optional Science.
ACT: Official test preparation and free practice tests: released ACT questions in the real test format.

ACT facts checked October 9, 2026. Every practice question on this page is original Dolphin practice written to match one ACT reporting category. None is a released ACT item.

ACT® is a trademark registered by ACT, Inc., which is not affiliated with, and does not endorse, Dolphin.

ACT Functions Practice

Functions on the ACT: the key numbers

What does ACT Functions test?

Practice ACT Functions questions

How to solve it

How to solve it

How to solve it

What mistakes do students make on Functions?

Squaring negatives without parentheses

Composing in the wrong order

Treating exponential functions as linear

How should you practice ACT Functions?

Questions about ACT Functions

Keep practicing for the ACT

Where these facts come from