ALEKS Pre-Calculus and Functions

Question 1

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

Accepted Answer

(3, 2)

Answer

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

Question 2

What is the period of y = sin(2x)?

Accepted Answer

π

Answer

The period of y = sin(bx) is 2π/b = 2π/2 = π.

Question 3

What is log₂(32)?

Accepted Answer

5

Answer

log₂(32) = 5 because 2⁵ = 32.

Question 4

Find the inverse of f(x) = 3x - 6.

Accepted Answer

f⁻¹(x) = (x + 6)/3

Answer

Replace f(x) with y, swap x and y, then solve: x = 3y - 6 → y = (x + 6)/3.

Question 5

Which of the following is an exponential growth function?

Accepted Answer

y = 3(1.5)ˣ

Answer

Exponential growth occurs when the base is greater than 1; y = 3(1.5)ˣ has base 1.5 > 1.

ALEKS - Assessment and Learning in Knowledge Spaces Practice Test