PRE CALCULUS Functions 4 — Questions and Answers
Question 1: If f(x) = 4x - 8, what is the value of x when f(x) = 0?
- 2 (Correct answer)
- -2
- 8
- 4
Correct answer: 2
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?
- A downward-opening parabola centered at the origin
- An upward-opening parabola centered at the origin (Correct answer)
- A cubic curve through the origin
- A line through the origin with positive slope
Correct answer: An upward-opening parabola centered at the origin
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)?
- 2a² + 4a - 1 (Correct answer)
- 2a² - 1
- 2a² + 4a + 2 - 3
- 2a + 2
Correct answer: 2a² + 4a - 1
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?
- f⁻¹(x) = x^(1/3) (Correct answer)
- f⁻¹(x) = 3x
- f⁻¹(x) = 1/x³
- f⁻¹(x) = x^(-3)
Correct answer: f⁻¹(x) = x^(1/3)
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?
- Vertex (1, 3), opens upward (Correct answer)
- Vertex (-1, 3), opens upward
- Vertex (1, -3), opens downward
- Vertex (1, 3), opens downward
Correct answer: Vertex (1, 3), opens upward
Vertex form f(x) = a(x-h)² + k gives vertex (h, k) = (1, 3); since a = 1 > 0 it opens upward.
Question 6: If f(4) = 7 and g(7) = -1, what is g(f(4))?
- -1 (Correct answer)
- 7
- 28
- 3
Correct answer: -1
g(f(4)) = g(7) = -1.
Question 7: Which condition guarantees that the inverse of a function f is also a function?
- f passes the vertical line test
- f is one-to-one (Correct answer)
- f has a y-intercept
- f is continuous
Correct answer: f is one-to-one
Only one-to-one functions have inverses that are also functions; the horizontal line test verifies this.
PRE CALCULUS Functions 4
If f(x) = 4x - 8, what is the value of x when f(x) = 0?