ALEKS Pre-Calculus and Functions 1 — Questions and Answers
Question 1: What is the vertex of the parabola y = (x - 3)² + 2?
- (3, 2) (Correct answer)
- (-3, 2)
- (3, -2)
- (2, 3)
Correct answer: (3, 2)
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)?
- π (Correct answer)
- 2π
- π/2
- 4π
Correct answer: π
The period of y = sin(bx) is 2π/b = 2π/2 = π.
Question 3: What is log₂(32)?
- 5 (Correct answer)
- 4
- 6
- 3
Correct answer: 5
log₂(32) = 5 because 2⁵ = 32.
Question 4: Find the inverse of f(x) = 3x - 6.
- f⁻¹(x) = (x + 6)/3 (Correct answer)
- f⁻¹(x) = (x - 6)/3
- f⁻¹(x) = 3x + 6
- f⁻¹(x) = x/3 - 6
Correct answer: f⁻¹(x) = (x + 6)/3
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?
- y = 3(1.5)ˣ (Correct answer)
- y = 3(0.5)ˣ
- y = 3x + 5
- y = 3x²
Correct answer: y = 3(1.5)ˣ
Exponential growth occurs when the base is greater than 1; y = 3(1.5)ˣ has base 1.5 > 1.
Question 6: What are the zeros of f(x) = x² - 4x + 3?
- x = 1 and x = 3 (Correct answer)
- x = -1 and x = -3
- x = 4 and x = 3
- x = 1 and x = -3
Correct answer: x = 1 and x = 3
Factor: (x - 1)(x - 3) = 0, giving x = 1 and x = 3.
ALEKS Pre-Calculus and Functions 1
What is the vertex of the parabola y = (x - 3)² + 2?