PRE CALCULUS Functions 4

Question 1

If f(x) = 4x - 8, what is the value of x when f(x) = 0?

Accepted Answer

2

Answer

Set 4x - 8 = 0 → 4x = 8 → x = 2.

Question 2

Which of the following graphs represents a function that is both even and has a minimum value?

Accepted Answer

An upward-opening parabola centered at the origin

Answer

An upward-opening parabola y = ax² (a > 0) is symmetric about the y-axis (even) and has a minimum at the vertex.

Question 3

Given f(x) = 2x² - 3, what is f(a + 1)?

Accepted Answer

2a² + 4a - 1

Answer

f(a+1) = 2(a+1)² - 3 = 2(a² + 2a + 1) - 3 = 2a² + 4a + 2 - 3 = 2a² + 4a - 1.

Question 4

What is the inverse of f(x) = x³?

Accepted Answer

f⁻¹(x) = x^(1/3)

Answer

To undo cubing, take the cube root: f⁻¹(x) = ∛x = x^(1/3).

Question 5

For f(x) = (x - 1)² + 3, what is the vertex and direction of opening?

Accepted Answer

Vertex (1, 3), opens upward

Answer

Vertex form f(x) = a(x-h)² + k gives vertex (h, k) = (1, 3); since a = 1 > 0 it opens upward.

PRE CALCULUS Practice Test