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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

Why is y=3x−2y=3x-2 a function of x?

Please select an answer first.

Correct answer: A

The correct answer is Each x-value produces 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: For every chosen x, the expression 3x−23x-2 gives one unique y.
  3. Check uniqueness and meaning: Confirm that each input has exactly one output and interpret the result in context.

For every chosen x, the expression 3x−23x-2 gives one unique y.

2. QuestionMultiple choice

What does the vertical line test show when every vertical line crosses a graph at most once?

Please select an answer first.

Correct answer: B

The correct answer is The graph represents y as a function of x..

  1. Identify the relation: List the inputs and outputs, or read the rule, table, mapping, or graph provided.
  2. Apply the function rule: At most one intersection means each x-value has at most one y-value.
  3. Check uniqueness and meaning: Confirm that each input has exactly one output and interpret the result in context.

At most one intersection means each x-value has at most one y-value.

3. QuestionMultiple choice

Is x=4x=4 a function of x when written as y in terms of x?

Please select an answer first.

Correct answer: C

The correct answer is No, because x=4 can correspond to many y-values..

  1. Identify the relation: List the inputs and outputs, or read the rule, table, mapping, or graph provided.
  2. Apply the function rule: The vertical line x=4 contains many points with the same x and different y values, so it fails the function test.
  3. Check uniqueness and meaning: Confirm that each input has exactly one output and interpret the result in context.

The vertical line x=4 contains many points with the same x and different y values, so it fails the function test.

4. QuestionMultiple choice

Why is y2=xy^2=x not a function of x over the real numbers?

Please select an answer first.

Correct answer: D

The correct answer is For a positive x, it can give two y-values..

  1. Identify the relation: List the inputs and outputs, or read the rule, table, mapping, or graph provided.
  2. Apply the function rule: For example, when x=4x=4, y=2y=2 or y=−2y=-2, so one input has two outputs.
  3. Check uniqueness and meaning: Confirm that each input has exactly one output and interpret the result in context.

For example, when x=4x=4, y=2y=2 or y=−2y=-2, so one input has two outputs.

5. QuestionMultiple choice

For f(x)=x2f(x)=x^2 with domain −2,−1,0,1,2\\{-2,-1,0,1,2\\}, what is the range?

Please select an answer first.

Correct answer: A

The correct answer is 0,1,4\\{0,1,4\\}.

  1. Identify the relation: List the inputs and outputs, or read the rule, table, mapping, or graph provided.
  2. Apply the function rule: The outputs are 4, 1, 0, 1, and 4; the distinct values are 0,1,4\\{0,1,4\\}.
  3. Check uniqueness and meaning: Confirm that each input has exactly one output and interpret the result in context.

The outputs are 4, 1, 0, 1, and 4; the distinct values are 0,1,4\\{0,1,4\\}.

6. QuestionMultiple choice

How can the inverse relation of a set of ordered pairs be found?

Please select an answer first.

Correct answer: B

The correct answer is Switch the coordinates in every ordered pair..

  1. Identify the relation: List the inputs and outputs, or read the rule, table, mapping, or graph provided.
  2. Apply the function rule: The inverse of (a,b)(a,b) contains (b,a)(b,a).
  3. Check uniqueness and meaning: Confirm that each input has exactly one output and interpret the result in context.

The inverse of (a,b)(a,b) contains (b,a)(b,a).

7. QuestionMultiple choice

If f(x)=2xf(x)=2x and g(x)=x+3g(x)=x+3, for which x are the outputs equal?

Please select an answer first.

Correct answer: C

The correct answer is x=3x=3.

  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 outputs equal: 2x=x+32x=x+3, so x=3x=3.
  3. Check uniqueness and meaning: Confirm that each input has exactly one output and interpret the result in context.

Set the outputs equal: 2x=x+32x=x+3, so x=3x=3.

8. QuestionMultiple choice

What is the zero of f(x)=4x−12f(x)=4x-12?

Please select an answer first.

Correct answer: D

The correct answer is 33.

  1. Identify the relation: List the inputs and outputs, or read the rule, table, mapping, or graph provided.
  2. Apply the function rule: A zero occurs when the output is 0: 4x−12=04x-12=0, so x=3x=3.
  3. Check uniqueness and meaning: Confirm that each input has exactly one output and interpret the result in context.

A zero occurs when the output is 0: 4x−12=04x-12=0, so x=3x=3.

9. QuestionMultiple choice

Is y=∣x∣y=|x| a function of x?

Please select an answer first.

Correct answer: A

The correct answer is Yes, each x has one absolute value..

  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 x has exactly one absolute value, so the relation is a function.
  3. Check uniqueness and meaning: Confirm that each input has exactly one output and interpret the result in context.

Every real x has exactly one absolute value, so the relation is a function.

10. QuestionMultiple choice

The graph of a function contains the point (2,9)(2,9). What does this mean?

Please select an answer first.

Correct answer: B

The correct answer is The output is 9 when the input is 2..

  1. Identify the relation: List the inputs and outputs, or read the rule, table, mapping, or graph provided.
  2. Apply the function rule: An ordered pair (x,y)(x,y) on a function graph means f(x)=yf(x)=y.
  3. Check uniqueness and meaning: Confirm that each input has exactly one output and interpret the result in context.

An ordered pair (x,y)(x,y) on a function graph means f(x)=yf(x)=y.

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