ALEKS Pre-Calculus and Functions 2 — Questions and Answers
Question 1: If sin(θ) = 3/5 and θ is in the first quadrant, what is cos(θ)?
- 4/5 (Correct answer)
- 3/4
- 5/3
- 5/4
Correct answer: 4/5
Using the Pythagorean identity: cos(θ) = √(1 - sin²θ) = √(1 - 9/25) = √(16/25) = 4/5.
Question 2: What is the range of f(x) = x² - 1?
- y ≥ -1 (Correct answer)
- all real numbers
- y ≥ 0
- y ≤ -1
Correct answer: y ≥ -1
Since x² ≥ 0 for all x, x² - 1 ≥ -1, so the range is y ≥ -1.
Question 3: What is the horizontal asymptote of y = 3/(x + 2)?
- y = 0 (Correct answer)
- y = 3
- x = -2
- y = 2
Correct answer: y = 0
As x → ±∞, 3/(x + 2) → 0, so the horizontal asymptote is y = 0.
Question 4: Which is true about even functions?
- f(-x) = f(x) (Correct answer)
- f(-x) = -f(x)
- f(x) = f(2x)
- f(0) = 0
Correct answer: f(-x) = f(x)
A function is even if f(-x) = f(x) for all x, meaning it is symmetric about the y-axis.
Question 5: What is 30° in radians?
- π/6 (Correct answer)
- π/4
- π/3
- π/2
Correct answer: π/6
30° × (π/180°) = π/6.
Question 6: Solve: log₃(x) = 4
- x = 81 (Correct answer)
- x = 12
- x = 64
- x = 34
Correct answer: x = 81
log₃(x) = 4 means 3⁴ = x = 81.
ALEKS Pre-Calculus and Functions 2
If sin(θ) = 3/5 and θ is in the first quadrant, what is cos(θ)?