Accuplacer College Placement ACCUPLACER Advanced Algebra and Functions Test

Question 1

What are the solutions to x² − 5x + 6 = 0?

Accepted Answer

x = 2 and x = 3

Answer

Factor as (x − 2)(x − 3) = 0, giving x = 2 and x = 3.

Question 2

Which of the following is the inverse function of f(x) = 3x − 6?

Accepted Answer

f⁻¹(x) = (x + 6)/3

Answer

Swap x and y in y = 3x − 6, then solve for y: x = 3y − 6 → y = (x + 6)/3.

Question 3

What is the vertex of the parabola y = (x − 3)² + 5?

Accepted Answer

(3, 5)

Answer

In vertex form y = (x − h)² + k, the vertex is (h, k) = (3, 5).

Question 4

Evaluate: log₂(32)

Accepted Answer

5

Answer

2⁵ = 32, so log₂(32) = 5.

Question 5

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

Accepted Answer

37

Answer

g(3) = 6, then f(6) = 6² + 1 = 37.

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