UTMA Functions and Graphing 1 — Questions and Answers
Question 1: Which of the following represents the domain of f(x) = √(x − 3)?
- x ≥ 3 (Correct answer)
- x > 3
- x ≤ 3
- All real numbers
Correct answer: x ≥ 3
The expression under a square root must be non-negative, so x − 3 ≥ 0, giving x ≥ 3.
Question 2: If f(x) = 2x + 1 and g(x) = x², what is (f ∘ g)(3)?
- 19 (Correct answer)
- 49
- 10
- 37
Correct answer: 19
g(3) = 9, then f(9) = 2(9) + 1 = 19.
Question 3: The graph of y = f(x − 2) + 3 is a transformation of y = f(x). Which transformation is applied?
- Shift right 2, up 3 (Correct answer)
- Shift left 2, up 3
- Shift right 2, down 3
- Shift left 2, down 3
Correct answer: Shift right 2, up 3
Replacing x with (x − 2) shifts the graph 2 units right, and adding 3 outside shifts it 3 units up.
Question 4: Which function is an even function?
- f(x) = x⁴ − 2x² (Correct answer)
- f(x) = x³ + x
- f(x) = x² + x
- f(x) = x³ − 1
Correct answer: f(x) = x⁴ − 2x²
A function is even if f(−x) = f(x); for x⁴ − 2x², f(−x) = x⁴ − 2x² = f(x).
Question 5: What is the range of f(x) = −x² + 4?
- (−∞, 4] (Correct answer)
- [4, ∞)
- (−∞, ∞)
- [−4, 4]
Correct answer: (−∞, 4]
Since −x² ≤ 0, the maximum value is 4, and the parabola opens downward, so f(x) ≤ 4.
Question 6: If f(x) = 3x − 5, what is f⁻¹(x)?
- (x + 5)/3 (Correct answer)
- (x − 5)/3
- 3x + 5
- (x − 3)/5
Correct answer: (x + 5)/3
To find the inverse, solve y = 3x − 5 for x: x = (y + 5)/3, so f⁻¹(x) = (x + 5)/3.
Question 7: The vertical line test is used to determine whether a graph represents:
- A function (Correct answer)
- An even function
- An invertible function
- A one-to-one function
Correct answer: A function
A graph represents a function if and only if every vertical line crosses the graph at most once.
UTMA Functions and Graphing 1
Which of the following represents the domain of f(x) = √(x − 3)?