Free ACT Math: Functions Questions and Answers

Question 1

If f(x) = 3x² - 5x + 2, what is the value of f(-3)?

Accepted Answer

44

Answer

-40

Answer

-10

Answer

14

Question 2

Let f(x) = x + 5 and g(x) = 2x - 3. What is f(g(x))?

Accepted Answer

2x + 2

Answer

2x + 7

Answer

2x² + 7x - 15

Answer

3x + 2

Question 3

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

Accepted Answer

8

Answer

2

Answer

10

Answer

14

Question 4

The graph of y = f(x) is shown in the xy-plane. Which of the following is the graph of y = f(x) - 2?

Accepted Answer

The graph of f(x) shifted 2 units down.

Answer

The graph of f(x) shifted 2 units to the right.

Answer

The graph of f(x) shifted 2 units to the left.

Answer

The graph of f(x) shifted 2 units up.

Question 5

If h(x) is a function, how does the graph of y = h(x + 4) relate to the graph of y = h(x)?

Accepted Answer

It is shifted 4 units to the left.

Answer

It is shifted 4 units to the right.

Answer

It is shifted 4 units up.

Answer

It is shifted 4 units down.

Question 6

The function f(x) = x² is transformed to g(x) = (x - 3)² + 5. Which statement describes this transformation?

Accepted Answer

A shift 3 units to the right and 5 units up.

Answer

A shift 3 units to the left and 5 units down.

Answer

A shift 3 units to the left and 5 units up.

Answer

A shift 3 units to the right and 5 units down.

Question 7

For the function f(x) = 2|x - 3|, what is the value of f(1)?

Accepted Answer

4

Answer

-4

Answer

-2

Answer

8