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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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1. Test

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

Is the mapping 1mapsto2,2mapsto4,3mapsto61\\mapsto2, 2\\mapsto4, 3\\mapsto6 a function?

Please select an answer first.

Correct answer: A

The correct answer is Yes, because 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: Each input is paired with one and only one output, which is the definition of a function.
  3. Check uniqueness and meaning: Confirm that each input has exactly one output and interpret the result in context.

Each input is paired with one and only one output, which is the definition of a function.

2. QuestionMultiple choice

What does the mapping 1mapsto2,2mapsto4,3mapsto61\\mapsto2, 2\\mapsto4, 3\\mapsto6 show?

Please select an answer first.

Correct answer: B

The correct answer is Each input is assigned 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: A function assigns exactly one output to each input; different inputs may share or have different outputs.
  3. Check uniqueness and meaning: Confirm that each input has exactly one output and interpret the result in context.

A function assigns exactly one output to each input; different inputs may share or have different outputs.

3. QuestionMultiple choice

Is the relation (1,2),(1,3)\\{(1,2),(1,3)\\} a function?

Please select an answer first.

Correct answer: C

The correct answer is No, because the input 1 has two outputs..

  1. Identify the relation: List the inputs and outputs, or read the rule, table, mapping, or graph provided.
  2. Apply the function rule: The same input 1 is paired with both 2 and 3, so the relation is not a function.
  3. Check uniqueness and meaning: Confirm that each input has exactly one output and interpret the result in context.

The same input 1 is paired with both 2 and 3, so the relation is not a function.

4. QuestionMultiple choice

The table has x-values 0,1,20,1,2 and y-values 5,5,75,5,7. Is it a function?

Please select an answer first.

Correct answer: D

The correct answer is Yes, because every x-value has exactly one y-value..

  1. Identify the relation: List the inputs and outputs, or read the rule, table, mapping, or graph provided.
  2. Apply the function rule: Repeated outputs are allowed; the important condition is that no input has more than one output.
  3. Check uniqueness and meaning: Confirm that each input has exactly one output and interpret the result in context.

Repeated outputs are allowed; the important condition is that no input has more than one output.

5. QuestionMultiple choice

What test can determine whether a graph represents y as a function of x?

Please select an answer first.

Correct answer: A

The correct answer is The vertical line test.

  1. Identify the relation: List the inputs and outputs, or read the rule, table, mapping, or graph provided.
  2. Apply the function rule: A graph represents y as a function of x when every vertical line intersects it at most once.
  3. Check uniqueness and meaning: Confirm that each input has exactly one output and interpret the result in context.

A graph represents y as a function of x when every vertical line intersects it at most once.

6. QuestionMultiple choice

What is the domain of the relation (1,5),(2,5),(4,3)\\{(1,5),(2,5),(4,3)\\}?

Please select an answer first.

Correct answer: B

The correct answer is 1,2,4\\{1,2,4\\}.

  1. Identify the relation: List the inputs and outputs, or read the rule, table, mapping, or graph provided.
  2. Apply the function rule: The domain is the set of all first coordinates: 1, 2, and 4.
  3. Check uniqueness and meaning: Confirm that each input has exactly one output and interpret the result in context.

The domain is the set of all first coordinates: 1, 2, and 4.

7. QuestionMultiple choice

What is the range of the relation (1,5),(2,5),(3,8)\\{(1,5),(2,5),(3,8)\\}?

Please select an answer first.

Correct answer: C

The correct answer is 5,8\\{5,8\\}.

  1. Identify the relation: List the inputs and outputs, or read the rule, table, mapping, or graph provided.
  2. Apply the function rule: The range is the set of distinct second coordinates, so it is 5,8\\{5,8\\}.
  3. Check uniqueness and meaning: Confirm that each input has exactly one output and interpret the result in context.

The range is the set of distinct second coordinates, so it is 5,8\\{5,8\\}.

8. QuestionMultiple choice

Which relation is not a function?

Please select an answer first.

Correct answer: D

The correct answer is (0,1),(0,4),(2,5)\\{(0,1),(0,4),(2,5)\\}.

  1. Identify the relation: List the inputs and outputs, or read the rule, table, mapping, or graph provided.
  2. Apply the function rule: The input 0 is paired with both 1 and 4, so it has two outputs.
  3. Check uniqueness and meaning: Confirm that each input has exactly one output and interpret the result in context.

The input 0 is paired with both 1 and 4, so it has two outputs.

9. QuestionMultiple choice

Which relation is a function?

Please select an answer first.

Correct answer: A

The correct answer is (−1,2),(0,2),(1,3)\\{(-1,2),(0,2),(1,3)\\}.

  1. Identify the relation: List the inputs and outputs, or read the rule, table, mapping, or graph provided.
  2. Apply the function rule: The inputs -1, 0, and 1 each appear once and each has exactly one output.
  3. Check uniqueness and meaning: Confirm that each input has exactly one output and interpret the result in context.

The inputs -1, 0, and 1 each appear once and each has exactly one output.

10. QuestionMultiple choice

For the rule y=x2y=x^2, what happens to each input?

Please select an answer first.

Correct answer: B

The correct answer is It is assigned exactly one output, its square..

  1. Identify the relation: List the inputs and outputs, or read the rule, table, mapping, or graph provided.
  2. Apply the function rule: Every real input has one square, so y=x2y=x^2 defines a function.
  3. Check uniqueness and meaning: Confirm that each input has exactly one output and interpret the result in context.

Every real input has one square, so y=x2y=x^2 defines a function.

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