Free ACT Math: Functions Questions and Answers

Question 1

If f(x) = 3x² − 2x + 1, what is f(−2)?

Accepted Answer

17

Answer

Substitute x = −2 into the function: f(−2) = 3(−2)² − 2(−2) + 1 = 3(4) + 4 + 1 = 12 + 4 + 1 = 17. Remember that (−2)² = +4 and −2(−2) = +4.

Question 2

Which of the following represents the inverse function of f(x) = 2x + 6?

Accepted Answer

f⁻¹(x) = (x − 6)/2

Answer

To find the inverse, swap x and y, then solve for y. Starting with y = 2x + 6: swap to get x = 2y + 6, then solve: x − 6 = 2y, so y = (x − 6)/2. Therefore f⁻¹(x) = (x − 6)/2.

Question 3

If g(x) = x + 3 and h(x) = x², what is h(g(2))?

Accepted Answer

25

Answer

This is a composition of functions. First evaluate the inner function: g(2) = 2 + 3 = 5. Then evaluate the outer function with this result: h(5) = 5² = 25. Always work from the inside out with function composition.

Question 4

A function f is defined as f(x) = |x − 3|. For what value(s) of x does f(x) = 5?

Accepted Answer

x = 8 and x = −2

Answer

Set up the absolute value equation: |x − 3| = 5. This gives two cases: x − 3 = 5 → x = 8, OR x − 3 = −5 → x = −2. Always check both cases when solving absolute value equations.

Question 5

The function f(x) = x² − 4x + 3 has zeros at x = 1 and x = 3. What is the x-coordinate of the vertex of this parabola?

Accepted Answer

x = 2

Answer

The vertex of a parabola lies on the axis of symmetry, which is the vertical line exactly halfway between the two zeros. Midpoint of x = 1 and x = 3: (1 + 3)/2 = 4/2 = 2. Alternatively, use the vertex formula x = −b/2a = −(−4)/(2·1) = 4/2 = 2.

ACT Practice Test

ACT Practice Test

Free ACT Math: Functions Questions and Answers