PRE CALCULUS Pre-Calculus Functions 2

Question 1

Which of the following best describes an even function?

Accepted Answer

f(-x) = f(x) for all x in the domain

Answer

An even function satisfies f(-x) = f(x), meaning it is symmetric about the y-axis.

Question 2

If f(x) = x² - 4 and g(x) = 2x + 1, what is (f ∘ g)(0)?

Accepted Answer

-3

Answer

g(0) = 1, then f(1) = 1 - 4 = -3.

Question 3

What is the inverse of f(x) = 3x - 6?

Accepted Answer

f⁻¹(x) = (x + 6)/3

Answer

Swap x and y then solve: x = 3y - 6 → y = (x + 6)/3.

Question 4

Which transformation shifts the graph of f(x) down by 5 units?

Accepted Answer

f(x) - 5

Answer

Subtracting 5 outside the function shifts the graph down 5 units.

Question 5

A function f has f(2) = 7 and f(5) = 7. Which property does this NOT necessarily imply?

Accepted Answer

f is one-to-one

Answer

A one-to-one function cannot have two different inputs mapping to the same output, but f(2) = f(5) = 7 shows this function is not one-to-one.

PRE CALCULUS Practice Test