ACT Practice Test: Video 1 Answers (25 Questions)

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

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 3

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 4

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.

Question 5

Which of these represents a function?

Accepted Answer

{(1,2),(2,3),(3,4)}

Answer

Each x-value maps to exactly one y-value only in the first set.