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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

If y=3x+2y=3x+2, what is y when x = 2?

Please select an answer first.

Correct answer: A

The correct answer is 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: Substitute x = 2: y = 3(2) + 2 = 8.
  3. Check the graph or value: The correct choice is 8.

Substitute x = 2: y = 3(2) + 2 = 8.

2. QuestionMultiple choice

A table has x-values 0, 1, 2 and y-values -1, 2, 5. Which rule fits?

Please select an answer first.

Correct answer: B

The correct answer is y=3x−1y=3x-1.

  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 output increases by 3 and the value at x = 0 is -1, so the rule is y = 3x - 1.
  3. Check the graph or value: The correct choice is y=3x−1y=3x-1.

The output increases by 3 and the value at x = 0 is -1, so the rule is y = 3x - 1.

3. QuestionMultiple choice

A mapping sends 2 to 5, 3 to 7, and 4 to 9. Which rule fits?

Please select an answer first.

Correct answer: C

The correct answer is y=2x+1y=2x+1.

  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 rule y = 2x + 1 produces 5, 7, and 9 for inputs 2, 3, and 4.
  3. Check the graph or value: The correct choice is y=2x+1y=2x+1.

The rule y = 2x + 1 produces 5, 7, and 9 for inputs 2, 3, and 4.

4. QuestionMultiple choice

A line crosses the y-axis at 4. What is its y-intercept?

Please select an answer first.

Correct answer: D

The correct answer is 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: The y-intercept is the y-value where the graph crosses the y-axis, so it is 4.
  3. Check the graph or value: The correct choice is 4.

The y-intercept is the y-value where the graph crosses the y-axis, so it is 4.

5. QuestionMultiple choice

What is the x-intercept of y=2x−6y=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 y = 0: 0 = 2x - 6, so 2x = 6 and x = 3.
  3. Check the graph or value: The correct choice is 3.

Set y = 0: 0 = 2x - 6, so 2x = 6 and x = 3.

6. QuestionMultiple choice

Which equation has slope -2 and y-intercept 5?

Please select an answer first.

Correct answer: B

The correct answer is y=−2x+5y=-2x+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: In y = mx + b, m = -2 and b = 5.
  3. Check the graph or value: The correct choice is y=−2x+5y=-2x+5.

In y = mx + b, m = -2 and b = 5.

7. QuestionMultiple choice

Which point lies on y=x−4y=x-4?

Please select an answer first.

Correct answer: C

The correct answer is (3, -1).

  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 x = 3, y = 3 - 4 = -1, so (3, -1) lies on the line.
  3. Check the graph or value: The correct choice is (3, -1).

For x = 3, y = 3 - 4 = -1, so (3, -1) lies on the line.

8. QuestionMultiple choice

A function table shows x = 0, 1, 2 and f(x) = 4, 6, 8. What is f(2)f(2)?

Please select an answer first.

Correct answer: D

The correct answer is 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 table directly gives the output 8 for the input 2.
  3. Check the graph or value: The correct choice is 8.

The table directly gives the output 8 for the input 2.

9. QuestionMultiple choice

A function models a school club meeting for times 0≤t≤80\le t\le8. What is the domain in context?

Please select an answer first.

Correct answer: A

The correct answer is All times from 0 through 8 hours, inclusive..

  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 restricted to the meaningful input interval from 0 to 8 hours.
  3. Check the graph or value: The correct choice is All times from 0 through 8 hours, inclusive..

The domain is restricted to the meaningful input interval from 0 to 8 hours.

10. QuestionMultiple choice

A cost model is C=5+2xC=5+2x for 0≤x≤40\le x\le4. What is the range of C?

Please select an answer first.

Correct answer: B

The correct answer is 5≤C≤135\le C\le13.

  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: At x = 0, C = 5; at x = 4, C = 13. Because the model increases, the range is 5 ≤ C ≤ 13.
  3. Check the graph or value: The correct choice is 5≤C≤135\le C\le13.

At x = 0, C = 5; at x = 4, C = 13. Because the model increases, the range is 5 ≤ C ≤ 13.

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