Wgu D667 – Precalculus | Objective
Assessment | (Oa) V1 And V2 | 2026
Update | Actual Questions And Answers
With Complete Solution
Section 1: Functions and Their Graphs
1. Which of the following represents a function?
A) {(1,2), (1,3), (2,4)}
B) {(1,2), (2,3), (3,4)}
C) {(1,2), (2,2), (2,3)}
D) {(1,1), (2,1), (2,2)}
Answer: B
Rationale: A function requires each input (x-value) to map to exactly one output (y-
value). In B, every x-value is unique. In A and C, x=1 and x=2 repeat with different y-
values, violating the definition of a function.
2. What is the domain of f(x) = √(x - 4)?
A) (-∞, ∞)
B) [4, ∞)
C) (4, ∞)
D) (-∞, 4]
Answer: B
Rationale: The expression under a square root must be non-negative: x - 4 ≥ 0 → x ≥ 4.
Therefore, the domain includes 4 and all real numbers greater than 4.
,3. What is the range of f(x) = x² - 3?
A) (-∞, ∞)
B) [-3, ∞)
C) (-3, ∞)
D) (-∞, -3]
Answer: B
Rationale: The minimum value of x² is 0, occurring at x=0. Therefore, the minimum of x²
- 3 is -3. The parabola opens upward, so the range is [-3, ∞).
4. Which test determines whether a graph represents a function?
A) Horizontal line test
B) Vertical line test
C) Diagonal line test
D) Origin test
Answer: B
Rationale: The vertical line test states that if any vertical line intersects the graph at
more than one point, the graph is not a function because an input has multiple outputs.
5. If f(x) = 2x + 1 and g(x) = x², what is (f ∘ g)(x)?
A) 2x² + 1
B) (2x + 1)²
C) 4x² + 4x + 1
D) x² + 2x + 1
Answer: A
Rationale: (f ∘ g)(x) = f(g(x)) = f(x²) = 2(x²) + 1 = 2x² + 1. This is composition, not
multiplication.
6. If f(x) = 3x - 2, what is f⁻¹(x)?
A) (x + 2)/3
B) (x - 2)/3
,C) 1/(3x - 2)
D) 3x + 2
Answer: A
Rationale: To find the inverse, replace f(x) with y: y = 3x - 2. Swap x and y: x = 3y - 2.
Solve for y: x + 2 = 3y → y = (x + 2)/3.
7. Which function is even?
A) f(x) = x³
B) f(x) = x² + 1
C) f(x) = x + 1
D) f(x) = sin(x)
Answer: B
Rationale: A function is even if f(-x) = f(x). For f(x) = x² + 1: f(-x) = (-x)² + 1 = x² + 1 =
f(x). Options A and D are odd, and C is neither.
8. The graph of y = f(x) + 3 represents which transformation?
A) Horizontal shift right 3
B) Vertical shift up 3
C) Horizontal shift left 3
D) Vertical stretch by 3
Answer: B
Rationale: Adding a constant outside the function shifts the graph vertically. f(x) + 3
moves the graph up by 3 units.
9. The graph of y = f(x - 2) represents which transformation?
A) Vertical shift down 2
B) Horizontal shift right 2
C) Horizontal shift left 2
D) Vertical stretch by 2
, Answer: B
Rationale: Replacing x with (x - 2) shifts the graph horizontally to the right by 2 units.
The transformation operates opposite to the sign inside the function.
10. What is the vertex of the parabola y = (x + 1)² - 4?
A) (1, -4)
B) (-1, -4)
C) (1, 4)
D) (-1, 4)
Answer: B
Rationale: The vertex form y = (x - h)² + k has vertex (h, k). Here, y = (x + 1)² - 4 = (x - (-
1))² - 4, so h = -1, k = -4.
11. What is the axis of symmetry for y = 2x² - 8x + 1?
A) x = 2
B) x = -2
C) x = 4
D) x = -4
Answer: A
Rationale: Axis of symmetry: x = -b/(2a). Here a=2, b=-8: x = -(-8)/(2·2) = 8/4 = 2.
12. Which function has a graph that is a V-shape?
A) y = x²
B) y = |x|
C) y = √x
D) y = 1/x
Answer: B
Rationale: The absolute value function y = |x| produces a V-shaped graph with vertex at
the origin. It reflects negative x-values to positive y-values.
Assessment | (Oa) V1 And V2 | 2026
Update | Actual Questions And Answers
With Complete Solution
Section 1: Functions and Their Graphs
1. Which of the following represents a function?
A) {(1,2), (1,3), (2,4)}
B) {(1,2), (2,3), (3,4)}
C) {(1,2), (2,2), (2,3)}
D) {(1,1), (2,1), (2,2)}
Answer: B
Rationale: A function requires each input (x-value) to map to exactly one output (y-
value). In B, every x-value is unique. In A and C, x=1 and x=2 repeat with different y-
values, violating the definition of a function.
2. What is the domain of f(x) = √(x - 4)?
A) (-∞, ∞)
B) [4, ∞)
C) (4, ∞)
D) (-∞, 4]
Answer: B
Rationale: The expression under a square root must be non-negative: x - 4 ≥ 0 → x ≥ 4.
Therefore, the domain includes 4 and all real numbers greater than 4.
,3. What is the range of f(x) = x² - 3?
A) (-∞, ∞)
B) [-3, ∞)
C) (-3, ∞)
D) (-∞, -3]
Answer: B
Rationale: The minimum value of x² is 0, occurring at x=0. Therefore, the minimum of x²
- 3 is -3. The parabola opens upward, so the range is [-3, ∞).
4. Which test determines whether a graph represents a function?
A) Horizontal line test
B) Vertical line test
C) Diagonal line test
D) Origin test
Answer: B
Rationale: The vertical line test states that if any vertical line intersects the graph at
more than one point, the graph is not a function because an input has multiple outputs.
5. If f(x) = 2x + 1 and g(x) = x², what is (f ∘ g)(x)?
A) 2x² + 1
B) (2x + 1)²
C) 4x² + 4x + 1
D) x² + 2x + 1
Answer: A
Rationale: (f ∘ g)(x) = f(g(x)) = f(x²) = 2(x²) + 1 = 2x² + 1. This is composition, not
multiplication.
6. If f(x) = 3x - 2, what is f⁻¹(x)?
A) (x + 2)/3
B) (x - 2)/3
,C) 1/(3x - 2)
D) 3x + 2
Answer: A
Rationale: To find the inverse, replace f(x) with y: y = 3x - 2. Swap x and y: x = 3y - 2.
Solve for y: x + 2 = 3y → y = (x + 2)/3.
7. Which function is even?
A) f(x) = x³
B) f(x) = x² + 1
C) f(x) = x + 1
D) f(x) = sin(x)
Answer: B
Rationale: A function is even if f(-x) = f(x). For f(x) = x² + 1: f(-x) = (-x)² + 1 = x² + 1 =
f(x). Options A and D are odd, and C is neither.
8. The graph of y = f(x) + 3 represents which transformation?
A) Horizontal shift right 3
B) Vertical shift up 3
C) Horizontal shift left 3
D) Vertical stretch by 3
Answer: B
Rationale: Adding a constant outside the function shifts the graph vertically. f(x) + 3
moves the graph up by 3 units.
9. The graph of y = f(x - 2) represents which transformation?
A) Vertical shift down 2
B) Horizontal shift right 2
C) Horizontal shift left 2
D) Vertical stretch by 2
, Answer: B
Rationale: Replacing x with (x - 2) shifts the graph horizontally to the right by 2 units.
The transformation operates opposite to the sign inside the function.
10. What is the vertex of the parabola y = (x + 1)² - 4?
A) (1, -4)
B) (-1, -4)
C) (1, 4)
D) (-1, 4)
Answer: B
Rationale: The vertex form y = (x - h)² + k has vertex (h, k). Here, y = (x + 1)² - 4 = (x - (-
1))² - 4, so h = -1, k = -4.
11. What is the axis of symmetry for y = 2x² - 8x + 1?
A) x = 2
B) x = -2
C) x = 4
D) x = -4
Answer: A
Rationale: Axis of symmetry: x = -b/(2a). Here a=2, b=-8: x = -(-8)/(2·2) = 8/4 = 2.
12. Which function has a graph that is a V-shape?
A) y = x²
B) y = |x|
C) y = √x
D) y = 1/x
Answer: B
Rationale: The absolute value function y = |x| produces a V-shaped graph with vertex at
the origin. It reflects negative x-values to positive y-values.
