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

To find f(-3), substitute -3 for every instance of x in the function f(x) = 3x² - 5x + 2. The calculation is f(-3) = 3(-3)² - 5(-3) + 2 = 3(9) + 15 + 2 = 27 + 15 + 2 = 44. Be careful with the signs, especially when squaring a negative number.

Question 2

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

Accepted Answer

2x + 2

Answer

The composition f(g(x)) means you substitute the entire function g(x) into the function f(x) wherever you see x. So, f(g(x)) = f(2x - 3). Now, substitute (2x - 3) into f(x) = x + 5, which gives (2x - 3) + 5. Simplifying this expression results in 2x + 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

This is a composition of functions evaluated at a point. First, evaluate the inner function: f(3) = (3)² + 1 = 9 + 1 = 10. Then, use this result as the input for the outer function: g(10) = 10 - 2 = 8. Therefore, g(f(3)) = 8.

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 transformation y = f(x) + k represents a vertical shift of the graph of f(x). When k is negative, the shift is downward. Therefore, y = f(x) - 2 is the graph of f(x) shifted down by 2 units.

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

The transformation y = f(x + k) represents a horizontal shift. Contrary to intuition, a positive k (like +4) shifts the graph to the left, and a negative k shifts it to the right. Therefore, y = h(x + 4) is the graph of h(x) shifted 4 units to the left.

ACT Practice Test

ACT Practice Test

FREE ACT Math: Functions Questions and Answers