PRE CALCULUS Pre-Calculus Functions 4

Question 1

A function f is one-to-one. Which tool best verifies this from its graph?

Accepted Answer

Horizontal line test

Answer

If every horizontal line crosses the graph at most once, the function is one-to-one.

Question 2

What is the period of f(x) = sin(3x)?

Accepted Answer

2π/3

Answer

The period of sin(bx) is 2π/b, so for b = 3 the period is 2π/3.

Question 3

If f(x) = x² and g(x) = √x (x ≥ 0), then (f ∘ g)(x) simplifies to:

Accepted Answer

x

Answer

f(g(x)) = f(√x) = (√x)² = x for x ≥ 0.

Question 4

The graph of f(x) = (x - 3)² + 1 has its vertex at:

Accepted Answer

(3, 1)

Answer

In vertex form f(x) = (x - h)² + k, the vertex is (h, k) = (3, 1).

Question 5

Which function has a vertical asymptote at x = -4?

Accepted Answer

f(x) = 1/(x + 4)

Answer

The denominator x + 4 equals zero at x = -4, creating a vertical asymptote there.

PRE CALCULUS Practice Test