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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

If f(x)=2x+3f(x)=2x+3, what is f(4)f(4)?

Please select an answer first.

Correct answer: A

The correct answer is 1111.

  1. Identify the relation: List the inputs and outputs, or read the rule, table, mapping, or graph provided.
  2. Apply the function rule: Substitute 4: f(4)=2(4)+3=11f(4)=2(4)+3=11.
  3. Check uniqueness and meaning: Confirm that each input has exactly one output and interpret the result in context.

Substitute 4: f(4)=2(4)+3=11f(4)=2(4)+3=11.

2. QuestionMultiple choice

If g(x)=x2−1g(x)=x^2-1, what is g(−3)g(-3)?

Please select an answer first.

Correct answer: B

The correct answer is 88.

  1. Identify the relation: List the inputs and outputs, or read the rule, table, mapping, or graph provided.
  2. Apply the function rule: Evaluate g(−3)=(−3)2−1=9−1=8g(-3)=(-3)^2-1=9-1=8.
  3. Check uniqueness and meaning: Confirm that each input has exactly one output and interpret the result in context.

Evaluate g(−3)=(−3)2−1=9−1=8g(-3)=(-3)^2-1=9-1=8.

3. QuestionMultiple choice

If h(x)=fracx2+4h(x)=\\frac{x}{2}+4, what is h(5)h(5)?

Please select an answer first.

Correct answer: C

The correct answer is frac132\\frac{13}{2}.

  1. Identify the relation: List the inputs and outputs, or read the rule, table, mapping, or graph provided.
  2. Apply the function rule: Substitute 5: h(5)=frac52+4=frac132h(5)=\\frac{5}{2}+4=\\frac{13}{2}.
  3. Check uniqueness and meaning: Confirm that each input has exactly one output and interpret the result in context.

Substitute 5: h(5)=frac52+4=frac132h(5)=\\frac{5}{2}+4=\\frac{13}{2}.

4. QuestionMultiple choice

If p(x)=−3x+1p(x)=-3x+1, what is p(−2)p(-2)?

Please select an answer first.

Correct answer: D

The correct answer is 77.

  1. Identify the relation: List the inputs and outputs, or read the rule, table, mapping, or graph provided.
  2. Apply the function rule: Evaluate p(−2)=−3(−2)+1=6+1=7p(-2)=-3(-2)+1=6+1=7.
  3. Check uniqueness and meaning: Confirm that each input has exactly one output and interpret the result in context.

Evaluate p(−2)=−3(−2)+1=6+1=7p(-2)=-3(-2)+1=6+1=7.

5. QuestionMultiple choice

If p(x)=4x−7p(x)=4x-7, which expression equals p(a)p(a)?

Please select an answer first.

Correct answer: A

The correct answer is 4a−74a-7.

  1. Identify the relation: List the inputs and outputs, or read the rule, table, mapping, or graph provided.
  2. Apply the function rule: Replace x with a in the rule, giving p(a)=4a−7p(a)=4a-7.
  3. Check uniqueness and meaning: Confirm that each input has exactly one output and interpret the result in context.

Replace x with a in the rule, giving p(a)=4a−7p(a)=4a-7.

6. QuestionMultiple choice

If q(x)=x2q(x)=x^2, what is q(3)+q(1)q(3)+q(1)?

Please select an answer first.

Correct answer: B

The correct answer is 1010.

  1. Identify the relation: List the inputs and outputs, or read the rule, table, mapping, or graph provided.
  2. Apply the function rule: Calculate q(3)=9q(3)=9 and q(1)=1q(1)=1, then add to get 10.
  3. Check uniqueness and meaning: Confirm that each input has exactly one output and interpret the result in context.

Calculate q(3)=9q(3)=9 and q(1)=1q(1)=1, then add to get 10.

7. QuestionMultiple choice

If f(x)=5x−2f(x)=5x-2, what is f(0)f(0)?

Please select an answer first.

Correct answer: C

The correct answer is −2-2.

  1. Identify the relation: List the inputs and outputs, or read the rule, table, mapping, or graph provided.
  2. Apply the function rule: Substitute x=0x=0: f(0)=5(0)−2=−2f(0)=5(0)-2=-2.
  3. Check uniqueness and meaning: Confirm that each input has exactly one output and interpret the result in context.

Substitute x=0x=0: f(0)=5(0)−2=−2f(0)=5(0)-2=-2.

8. QuestionMultiple choice

What is the output when y=3x+1y=3x+1 and x=−4x=-4?

Please select an answer first.

Correct answer: D

The correct answer is −11-11.

  1. Identify the relation: List the inputs and outputs, or read the rule, table, mapping, or graph provided.
  2. Apply the function rule: Substitute x=−4x=-4: y=3(−4)+1=−11y=3(-4)+1=-11.
  3. Check uniqueness and meaning: Confirm that each input has exactly one output and interpret the result in context.

Substitute x=−4x=-4: y=3(−4)+1=−11y=3(-4)+1=-11.

9. QuestionMultiple choice

If f(x)=x+6f(x)=x+6 and f(x)=14f(x)=14, what is x?

Please select an answer first.

Correct answer: A

The correct answer is 88.

  1. Identify the relation: List the inputs and outputs, or read the rule, table, mapping, or graph provided.
  2. Apply the function rule: Solve x+6=14x+6=14, giving x=8x=8.
  3. Check uniqueness and meaning: Confirm that each input has exactly one output and interpret the result in context.

Solve x+6=14x+6=14, giving x=8x=8.

10. QuestionMultiple choice

A function table shows inputs 0,1,20,1,2 with outputs 4,6,94,6,9. What is the output for input 2?

Please select an answer first.

Correct answer: B

The correct answer is 99.

  1. Identify the relation: List the inputs and outputs, or read the rule, table, mapping, or graph provided.
  2. Apply the function rule: Read the row or column corresponding to input 2; its output is 9.
  3. Check uniqueness and meaning: Confirm that each input has exactly one output and interpret the result in context.

Read the row or column corresponding to input 2; its output is 9.

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