Grade 8 Math Practice Test: Comparing Functions and Describing Graphs
- Comparing Functions
- 10 questions
- 15 minutes
This test covers what makes a relation a function, comparing functions given as equations, tables and descriptions, and matching graphs to real situations. Tip: in y = mx + b, m is the rate of change and b is the initial value.
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
Which set of ordered pairs is a function?
Correct answer: D
In a function each input has exactly one output. In {(1, 3), (2, 3), (3, 3)} every input appears once; the same output for different inputs is allowed. The other sets repeat an input with two outputs.
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Question 2
Function A is y = 3x + 2. Function B is given by the table.
x 0 1 2 y 5 9 13 Which function has the greater rate of change?
Correct answer: C
In the table, y increases by 4 each time x increases by 1, so B has rate of change 4. A has rate of change 3. The 5 in the table is B’s initial value, not its rate.
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Question 3
Function A is y = −2x + 7. Function B is a line that passes through (0, 4) and (2, 0). Which function has the greater initial value, and by how much?
Correct answer: B
The initial value is the y-value at x = 0: 7 for A and 4 for B, so A is greater by 3. 11 comes from treating B’s initial value as −4.
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Question 4
Which function is NOT linear?
Correct answer: D
y = x2 + 1 has x squared, so its graph is a curve. y = 7 is a horizontal line with rate of change 0, and the others can be written as y = mx + b.
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Question 5
A function is shown in the table.
x 1 2 3 4 y 2 4 8 16 Which statement describes the function?
Correct answer: B
The y-values increase by 2, 4 and 8, so the rate of change is not constant and the function is not linear. A constant step in x alone does not make a function linear.
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Question 6
Maya rode her bike from home to the park at a steady speed, stayed at the park for a while, then rode home faster than she had ridden there. Which describes the graph of her distance from home over time?
Correct answer: C
Riding away makes the distance rise, waiting keeps it constant, and riding home faster makes it fall with a steeper slope. A less steep fall would mean a slower ride home.
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Question 7
A linear function passes through (2, 11) and (6, 23). Which equation represents it?
Correct answer: A
The rate of change is (23 − 11) ÷ (6 − 2) = 12 ÷ 4 = 3. Then 11 = 3 · 2 + b gives b = 5. y = 3x + 11 uses the y-value 11 as the initial value, but 11 belongs to x = 2, not x = 0.
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Question 8
The cost of a taxi ride is C = 2.5m + 4, where m is the number of miles. What does the 4 represent?
Correct answer: A
The 4 is the initial value: when m = 0 the cost is already $4. The cost per mile is the rate of change, 2.5.
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Question 9
Gym plan A costs $30 plus $5 per class. Plan B costs $10 per class. For 10 classes, which plan costs less, and by how much?
Correct answer: A
Plan A: 30 + 5 · 10 = $80. Plan B: 10 · 10 = $100. Plan A is $20 cheaper. The plans cost the same only at 6 classes.
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Question 10
How does y change in the function y = −0.5x + 8 as x increases?
Correct answer: C
The rate of change is −0.5, so y goes down 0.5 for every 1 unit x goes up. The 8 is the initial value, not the rate.
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