ALEKS Pre-Calculus and Functions 2

Question 1

If sin(θ) = 3/5 and θ is in the first quadrant, what is cos(θ)?

Accepted Answer

4/5

Answer

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?

Accepted Answer

y ≥ -1

Answer

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)?

Accepted Answer

y = 0

Answer

As x → ±∞, 3/(x + 2) → 0, so the horizontal asymptote is y = 0.

Question 4

Which is true about even functions?

Accepted Answer

f(-x) = f(x)

Answer

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?

Accepted Answer

π/6

Answer

30° × (π/180°) = π/6.

ALEKS - Assessment and Learning in Knowledge Spaces Practice Test