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Functions and Relations Practice Tests

These Grade 8 Math practice tests cover relations, mappings, function rules, domains, ranges, function notation, graphs, tables, and real-world models.

Skills covered

  • Determining whether a relation is a function
  • Reading mappings, ordered pairs, tables, and graphs
  • Finding domains and ranges and applying the vertical line test
  • Evaluating function notation such as \(f(x)\)
  • Modeling ticket costs, temperature, population, pay, plans, and other relationships

How to use these practice tests

Identify the input and output first. Then check that each input has exactly one output, evaluate the rule carefully, and interpret the domain and range in context.

For more Grade 8 Math practice, return to the Grade 8 Math category.

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Grade 8 Functions and Relations Practice Tests

Practice Grade 8 Math questions about functions, relations, mappings, domains, ranges, function notation, graphs, tables, and real-world models.

Choose the best answer for each question. Check inputs, outputs, domains, ranges, and the one-output-per-input rule.

10 Questions
0/10 Questions0 %
Correct 0
Incorrect 0
Unanswered 10
1. QuestionMultiple choice

A school charges $12 plus $5 for each event ticket. Which equation gives the total cost C for n tickets?

Please select an answer first.

Correct answer: A

The correct answer is C=5n+12C=5n+12.

  1. Identify the relation: List the inputs and outputs, or read the rule, table, mapping, or graph provided.
  2. Apply the function rule: The fixed starting fee is 12 and the rate is 5 dollars per ticket, so C=5n+12C=5n+12.
  3. Check uniqueness and meaning: Confirm that each input has exactly one output and interpret the result in context.

The fixed starting fee is 12 and the rate is 5 dollars per ticket, so C=5n+12C=5n+12.

2. QuestionMultiple choice

Using C=5n+12C=5n+12, what is the cost of 4 tickets?

Please select an answer first.

Correct answer: B

The correct answer is 3232 dollars.

  1. Identify the relation: List the inputs and outputs, or read the rule, table, mapping, or graph provided.
  2. Apply the function rule: Substitute n=4n=4: C=5(4)+12=32C=5(4)+12=32.
  3. Check uniqueness and meaning: Confirm that each input has exactly one output and interpret the result in context.

Substitute n=4n=4: C=5(4)+12=32C=5(4)+12=32.

3. QuestionMultiple choice

Temperature is modeled by T=2h+60T=2h+60. What is the temperature after 3 hours?

Please select an answer first.

Correct answer: C

The correct answer is 6666 degrees.

  1. Identify the relation: List the inputs and outputs, or read the rule, table, mapping, or graph provided.
  2. Apply the function rule: Substitute h=3h=3: T=2(3)+60=66T=2(3)+60=66.
  3. Check uniqueness and meaning: Confirm that each input has exactly one output and interpret the result in context.

Substitute h=3h=3: T=2(3)+60=66T=2(3)+60=66.

4. QuestionMultiple choice

In a taxi model, the cost depends on the number of miles traveled. Which is the independent variable?

Please select an answer first.

Correct answer: D

The correct answer is The number of miles traveled.

  1. Identify the relation: List the inputs and outputs, or read the rule, table, mapping, or graph provided.
  2. Apply the function rule: The number of miles is the input that determines the total cost, so it is the independent variable.
  3. Check uniqueness and meaning: Confirm that each input has exactly one output and interpret the result in context.

The number of miles is the input that determines the total cost, so it is the independent variable.

5. QuestionMultiple choice

A population is modeled by P=500+25tP=500+25t. What is the population after 8 years?

Please select an answer first.

Correct answer: A

The correct answer is 700700.

  1. Identify the relation: List the inputs and outputs, or read the rule, table, mapping, or graph provided.
  2. Apply the function rule: Substitute t=8t=8: P=500+25(8)=700P=500+25(8)=700.
  3. Check uniqueness and meaning: Confirm that each input has exactly one output and interpret the result in context.

Substitute t=8t=8: P=500+25(8)=700P=500+25(8)=700.

6. QuestionMultiple choice

A function maps hours worked to pay. Why is it a function when each number of hours has one pay amount?

Please select an answer first.

Correct answer: B

The correct answer is Each input has exactly one output..

  1. Identify the relation: List the inputs and outputs, or read the rule, table, mapping, or graph provided.
  2. Apply the function rule: The function rule requires one output for every input; different inputs may sometimes have the same output.
  3. Check uniqueness and meaning: Confirm that each input has exactly one output and interpret the result in context.

The function rule requires one output for every input; different inputs may sometimes have the same output.

7. QuestionMultiple choice

A water level is modeled by W=80−3tW=80-3t. How much water remains after 10 minutes?

Please select an answer first.

Correct answer: C

The correct answer is 5050 liters.

  1. Identify the relation: List the inputs and outputs, or read the rule, table, mapping, or graph provided.
  2. Apply the function rule: Substitute t=10t=10: W=80−3(10)=50W=80-3(10)=50.
  3. Check uniqueness and meaning: Confirm that each input has exactly one output and interpret the result in context.

Substitute t=10t=10: W=80−3(10)=50W=80-3(10)=50.

8. QuestionMultiple choice

A mapping assigns each number of hours worked to one paycheck amount. What does this mapping represent?

Please select an answer first.

Correct answer: D

The correct answer is A function.

  1. Identify the relation: List the inputs and outputs, or read the rule, table, mapping, or graph provided.
  2. Apply the function rule: Every input, the number of hours, is assigned one output, the paycheck amount.
  3. Check uniqueness and meaning: Confirm that each input has exactly one output and interpret the result in context.

Every input, the number of hours, is assigned one output, the paycheck amount.

9. QuestionMultiple choice

Plan A costs 10+2m10+2m dollars and Plan B costs 4m4m dollars. At how many miles m are the costs equal?

Please select an answer first.

Correct answer: A

The correct answer is m=5m=5.

  1. Identify the relation: List the inputs and outputs, or read the rule, table, mapping, or graph provided.
  2. Apply the function rule: Set the costs equal: 10+2m=4m10+2m=4m, so 10=2m10=2m and m=5m=5.
  3. Check uniqueness and meaning: Confirm that each input has exactly one output and interpret the result in context.

Set the costs equal: 10+2m=4m10+2m=4m, so 10=2m10=2m and m=5m=5.

10. QuestionMultiple choice

On a graph of hours worked versus pay, what does the point (6,90)(6,90) mean?

Please select an answer first.

Correct answer: B

The correct answer is Working 6 hours results in $90 pay..

  1. Identify the relation: List the inputs and outputs, or read the rule, table, mapping, or graph provided.
  2. Apply the function rule: The first coordinate is the input hours and the second is the output pay.
  3. Check uniqueness and meaning: Confirm that each input has exactly one output and interpret the result in context.

The first coordinate is the input hours and the second is the output pay.

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