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Functions and Graphs Practice Tests

These Grade 9 Math practice tests cover function definitions, domain and range, function notation, ordered pairs, mappings, tables, vertical line tests, slope, intercepts, linear and nonlinear relationships, transformations, sequences, and real-world function models.

Skills covered

  • Determining whether a relation or graph is a function
  • Finding domains, ranges, outputs, zeros, and intercepts
  • Evaluating function notation from rules, tables, and mappings
  • Interpreting slope, constant rate of change, parallel lines, and transformations
  • Building and analyzing linear models for cost, savings, temperature, population, and travel

How to use these practice tests

Identify the input and output first. Then evaluate the rule, compare changes in the table, read graph features, apply the vertical line test, and check whether the domain and range make sense in context.

For more Grade 9 Math practice, return to the Grade 9 Math category.

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1. Test

Grade 9 Functions and Graphs Practice Tests

Practice Grade 9 Math questions about functions, domain, range, function notation, tables, mappings, graphs, slope, intercepts, transformations, and linear models.

Choose the best answer. Identify inputs and outputs, evaluate function rules carefully, read graph features, and interpret the model in context.

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

What makes a relation a function?

Please select an answer first.

Correct answer: A

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

  1. Identify the function representation: Determine whether the information is given as a rule, table, mapping, graph, ordered pairs, or a context.
  2. Connect inputs and outputs: A function assigns one and only one output to each input, although multiple inputs may share an output.
  3. Check the graph or value: The correct choice is Each input has exactly one output..

A function assigns one and only one output to each input, although multiple inputs may share an output.

2. QuestionMultiple choice

What is the domain of a function?

Please select an answer first.

Correct answer: B

The correct answer is The set of possible input values..

  1. Identify the function representation: Determine whether the information is given as a rule, table, mapping, graph, ordered pairs, or a context.
  2. Connect inputs and outputs: The domain contains the values that can be used as inputs to the function.
  3. Check the graph or value: The correct choice is The set of possible input values..

The domain contains the values that can be used as inputs to the function.

3. QuestionMultiple choice

What is the range of a function?

Please select an answer first.

Correct answer: C

The correct answer is The set of possible output values..

  1. Identify the function representation: Determine whether the information is given as a rule, table, mapping, graph, ordered pairs, or a context.
  2. Connect inputs and outputs: The range contains the values produced by the function for the allowed inputs.
  3. Check the graph or value: The correct choice is The set of possible output values..

The range contains the values produced by the function for the allowed inputs.

4. QuestionMultiple choice

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

Please select an answer first.

Correct answer: D

The correct answer is 11.

  1. Identify the function representation: Determine whether the information is given as a rule, table, mapping, graph, ordered pairs, or a context.
  2. Connect inputs and outputs: Substitute 4 for x: f(4) = 2(4) + 3 = 11.
  3. Check the graph or value: The correct choice is 11.

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

5. QuestionMultiple choice

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

Please select an answer first.

Correct answer: A

The correct answer is 5.

  1. Identify the function representation: Determine whether the information is given as a rule, table, mapping, graph, ordered pairs, or a context.
  2. Connect inputs and outputs: Square -2 to get 4, then add 1: g(-2) = 5.
  3. Check the graph or value: The correct choice is 5.

Square -2 to get 4, then add 1: g(-2) = 5.

6. QuestionMultiple choice

Which relation is a function?

Please select an answer first.

Correct answer: B

The correct answer is The ordered pairs (1, 2), (2, 4), and (3, 6)..

  1. Identify the function representation: Determine whether the information is given as a rule, table, mapping, graph, ordered pairs, or a context.
  2. Connect inputs and outputs: Each input in the first relation appears once and has exactly one output.
  3. Check the graph or value: The correct choice is The ordered pairs (1, 2), (2, 4), and (3, 6)..

Each input in the first relation appears once and has exactly one output.

7. QuestionMultiple choice

Which relation is not a function?

Please select an answer first.

Correct answer: C

The correct answer is The ordered pairs (1, 2), (1, 4), and (3, 6)..

  1. Identify the function representation: Determine whether the information is given as a rule, table, mapping, graph, ordered pairs, or a context.
  2. Connect inputs and outputs: Input 1 is paired with both 2 and 4, so the relation violates the definition of a function.
  3. Check the graph or value: The correct choice is The ordered pairs (1, 2), (1, 4), and (3, 6)..

Input 1 is paired with both 2 and 4, so the relation violates the definition of a function.

8. QuestionMultiple choice

What does the vertical line test determine?

Please select an answer first.

Correct answer: D

The correct answer is Whether a graph represents a function of x..

  1. Identify the function representation: Determine whether the information is given as a rule, table, mapping, graph, ordered pairs, or a context.
  2. Connect inputs and outputs: If any vertical line crosses a graph more than once, one input has multiple outputs and the graph is not a function of x.
  3. Check the graph or value: The correct choice is Whether a graph represents a function of x..

If any vertical line crosses a graph more than once, one input has multiple outputs and the graph is not a function of x.

9. QuestionMultiple choice

What is the domain of the table with x-values -1, 0, and 3?

Please select an answer first.

Correct answer: A

The correct answer is {-1, 0, 3}.

  1. Identify the function representation: Determine whether the information is given as a rule, table, mapping, graph, ordered pairs, or a context.
  2. Connect inputs and outputs: The domain is the set of listed input values, so it is {-1, 0, 3}.
  3. Check the graph or value: The correct choice is {-1, 0, 3}.

The domain is the set of listed input values, so it is {-1, 0, 3}.

10. QuestionMultiple choice

What is the range of the table with y-values 2, 5, and 8?

Please select an answer first.

Correct answer: B

The correct answer is {2, 5, 8}.

  1. Identify the function representation: Determine whether the information is given as a rule, table, mapping, graph, ordered pairs, or a context.
  2. Connect inputs and outputs: The range is the set of listed output values, so it is {2, 5, 8}.
  3. Check the graph or value: The correct choice is {2, 5, 8}.

The range is the set of listed output values, so it is {2, 5, 8}.

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