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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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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

Is the relation y2=xy^2=x a function of x?

Please select an answer first.

Correct answer: A

The correct answer is No, because one positive x-value can produce two y-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: For example, x = 4 gives y = 2 and y = -2, so one input has two outputs.
  3. Check the graph or value: The correct choice is No, because one positive x-value can produce two y-values..

For example, x = 4 gives y = 2 and y = -2, so one input has two outputs.

2. QuestionMultiple choice

Is the circle x2+y2=9x^2+y^2=9 a function of x?

Please select an answer first.

Correct answer: B

The correct answer is No, because many vertical lines cross it twice..

  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 vertical line test fails for a circle because most vertical lines intersect it at two points.
  3. Check the graph or value: The correct choice is No, because many vertical lines cross it twice..

The vertical line test fails for a circle because most vertical lines intersect it at two points.

3. QuestionMultiple choice

Which equation represents y as a function of x?

Please select an answer first.

Correct answer: C

The correct answer is y=x2y=x^2.

  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: For each x, y = x squared gives exactly one output.
  3. Check the graph or value: The correct choice is y=x2y=x^2.

For each x, y = x squared gives exactly one output.

4. QuestionMultiple choice

Which table does not represent a function?

Please select an answer first.

Correct answer: D

The correct answer is x: 2, 2; y: 5, 7..

  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 input 2 is paired with two different outputs, 5 and 7.
  3. Check the graph or value: The correct choice is x: 2, 2; y: 5, 7..

The input 2 is paired with two different outputs, 5 and 7.

5. QuestionMultiple choice

If f(x)=2x+1f(x)=2x+1 and g(x)=x+4g(x)=x+4, for what x are they equal?

Please select an answer first.

Correct answer: A

The correct answer is 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: Set the functions equal: 2x + 1 = x + 4, so x = 3.
  3. Check the graph or value: The correct choice is 3.

Set the functions equal: 2x + 1 = x + 4, so x = 3.

6. QuestionMultiple choice

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

Please select an answer first.

Correct answer: B

The correct answer is 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: Substitute x = 4 into f(x) = x + 2 to get 6.
  3. Check the graph or value: The correct choice is 6.

Substitute x = 4 into f(x) = x + 2 to get 6.

7. QuestionMultiple choice

If f(x)=x−5f(x)=x-5, which rule gives the inverse function?

Please select an answer first.

Correct answer: C

The correct answer is f−1(x)=x+5f^{-1}(x)=x+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: The inverse undoes subtracting 5 by adding 5, so the inverse rule is x + 5.
  3. Check the graph or value: The correct choice is f−1(x)=x+5f^{-1}(x)=x+5.

The inverse undoes subtracting 5 by adding 5, so the inverse rule is x + 5.

8. QuestionMultiple choice

What is the y-intercept of y=x2−4y=x^2-4?

Please select an answer first.

Correct answer: D

The correct answer is (0, -4).

  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: Set x = 0: y = 0 squared - 4 = -4, giving the point (0, -4).
  3. Check the graph or value: The correct choice is (0, -4).

Set x = 0: y = 0 squared - 4 = -4, giving the point (0, -4).

9. QuestionMultiple choice

What is the zero of f(x)=2x+6f(x)=2x+6?

Please select an answer first.

Correct answer: A

The correct answer is -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: Set f(x) = 0: 2x + 6 = 0, so x = -3.
  3. Check the graph or value: The correct choice is -3.

Set f(x) = 0: 2x + 6 = 0, so x = -3.

10. QuestionMultiple choice

Which statement best describes a function?

Please select an answer first.

Correct answer: B

The correct answer is It assigns exactly one output to every allowed input..

  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 defining condition is one output for each input; a function can be linear, nonlinear, increasing, decreasing, or constant.
  3. Check the graph or value: The correct choice is It assigns exactly one output to every allowed input..

The defining condition is one output for each input; a function can be linear, nonlinear, increasing, decreasing, or constant.

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