PRE CALCULUS Pre-Calculus Functions 5

Question 1

Which statement about the composition (f ∘ g)(x) is always true?

Accepted Answer

The domain of f ∘ g is a subset of the domain of g

Answer

The domain of f ∘ g consists of all x in the domain of g such that g(x) is in the domain of f.

Question 2

For f(x) = 2|x - 1| - 3, what is the minimum value of f?

Accepted Answer

-3

Answer

The absolute value term is minimized at x = 1, giving f(1) = 0 - 3 = -3.

Question 3

If f is an even function and f(3) = 7, what is f(-3)?

Accepted Answer

7

Answer

Even functions satisfy f(-x) = f(x), so f(-3) = f(3) = 7.

Question 4

The function f(x) = x³ is stretched vertically by a factor of 4. The new function is:

Accepted Answer

4x³

Answer

A vertical stretch by factor 4 multiplies the output: new function = 4·f(x) = 4x³.

Question 5

Which pair of functions are inverses of each other?

Accepted Answer

f(x) = 2x + 3 and g(x) = (x - 3)/2

Answer

Composing them: f(g(x)) = 2·(x-3)/2 + 3 = x - 3 + 3 = x, confirming they are inverses.

PRE CALCULUS Practice Test