Algebra 1 Practice Test: Function Notation, Domain and Range
- Functions, Domain and Range
- 10 questions
- 13 minutes
These 10 questions cover evaluating f(x), reading what a function value means and finding domain and range. Tip: for the domain, ask which x-values would make the expression undefined.
Tap an option to mark your answer. You can change your mind, or tap the same option again to leave the question blank. The correct answers and explanations appear when you finish the test.Tap an option to answer; tap it again to leave the question blank.
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Question 1
If f(x) = 3x − 5, what is f(−2)?
Correct answer: B
Replace x with −2: 3(−2) − 5 = −6 − 5 = −11. Getting −1 comes from adding 5 instead of subtracting it.
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Question 2
Which relation is not a function?
Correct answer: D
In a function each input has exactly one output. Here the input 1 is paired with both 2 and 5. Repeated outputs, as in the first set, are allowed.
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Question 3
What is the domain of f(x) = x − 4?
Correct answer: A
The expression under a square root cannot be negative, so x − 4 ≥ 0 and x ≥ 4. The value 4 itself is allowed because 0 = 0.
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Question 4
What is the range of y = x2 + 3?
Correct answer: C
Since x2 is never negative, the smallest value of x2 + 3 is 3 (at x = 0), and the outputs grow without bound. So the range is y ≥ 3.
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Question 5
If g(x) = x2 − 2x, which expression equals g(a + 1)?
Correct answer: B
(a + 1)2 − 2(a + 1) = a2 + 2a + 1 − 2a − 2 = a2 − 1. The trap a2 − 2a + 1 is g(a) + 1, not g(a + 1).
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Question 6
If f(x) = 2x + 7, for what value of x is f(x) = 19?
Correct answer: A
Solve 2x + 7 = 19: 2x = 12, so x = 6. The value 45 is f(19), which answers a different question.
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Question 7
A climbing gym charges a $25 sign-up fee plus $15 per month. The total cost is C(m) = 25 + 15m, where m is the number of months.
What does C(6) = 115 mean?
Correct answer: D
The input m = 6 is the number of months and the output 115 is the total cost in dollars: 25 + 15(6) = 115.
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Question 8
What is the domain of h(x) = 5x + 3?
Correct answer: D
Division by zero is undefined, and x + 3 = 0 when x = −3. Every other real number works, including values less than −3.
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Question 9
What is the range of f(x) = −|x| + 4?
Correct answer: A
|x| is never negative, so −|x| is at most 0 and −|x| + 4 is at most 4. The graph is an upside-down V with its highest point at (0, 4).
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Question 10
A function is given by the set {(−3, 4), (0, 4), (2, −1), (5, 7)}. What is its domain?
Correct answer: B
The domain is the set of first coordinates (inputs). The set {−1, 4, 7} lists the outputs, which is the range.
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