PRE CALCULUS Functions 2

Question 1

Which of the following is the definition of a one-to-one function?

Accepted Answer

Each output has exactly one input

Answer

A one-to-one (injective) function means each output value corresponds to exactly one input value.

Question 2

If f(x) = 2x - 3, what is f⁻¹(x)?

Accepted Answer

(x + 3) / 2

Answer

To find the inverse, swap x and y in y = 2x - 3 and solve for y: x = 2y - 3 → y = (x + 3)/2.

Question 3

Given f(x) = x² and g(x) = x + 1, what is (f ∘ g)(x)?

Accepted Answer

(x + 1)² and x² + 2x + 1 are the same

Answer

(f ∘ g)(x) = f(g(x)) = (x+1)² = x² + 2x + 1, so options B and C are identical expressions.

Question 4

What is the range of f(x) = |x| - 4?

Accepted Answer

y ≥ -4

Answer

Since |x| ≥ 0 for all x, |x| - 4 ≥ -4, so the range is [-4, ∞).

Question 5

Which transformation maps f(x) to f(x - 3) + 2?

Accepted Answer

Shift right 3, up 2

Answer

Replacing x with (x - 3) shifts the graph right 3 units, and adding 2 shifts it up 2 units.

PRE CALCULUS Practice Test