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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

A cell plan is y=25+0.10my=25+0.10m. What does the y-intercept 25 represent?

Please select an answer first.

Correct answer: A

The correct answer is The fixed starting cost of the plan..

  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: When m = 0, the cost is 25, so 25 is the fixed starting charge.
  3. Check the graph or value: The correct choice is The fixed starting cost of the plan..

When m = 0, the cost is 25, so 25 is the fixed starting charge.

2. QuestionMultiple choice

Savings are modeled by y=40+15wy=40+15w. How much is saved after 6 weeks?

Please select an answer first.

Correct answer: B

The correct answer is $130.

  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 w = 6: y = 40 + 15(6) = 40 + 90 = 130 dollars.
  3. Check the graph or value: The correct choice is $130.

Substitute w = 6: y = 40 + 15(6) = 40 + 90 = 130 dollars.

3. QuestionMultiple choice

Use F=1.8C+32F=1.8C+32. What is F when C = 10?

Please select an answer first.

Correct answer: C

The correct answer is 50.

  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 C = 10: F = 1.8(10) + 32 = 18 + 32 = 50.
  3. Check the graph or value: The correct choice is 50.

Substitute C = 10: F = 1.8(10) + 32 = 18 + 32 = 50.

4. QuestionMultiple choice

A taxi model is C=3+2.5mC=3+2.5m. What does the slope 2.5 represent?

Please select an answer first.

Correct answer: D

The correct answer is The cost per mile..

  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 coefficient of m gives the change in cost for each additional mile.
  3. Check the graph or value: The correct choice is The cost per mile..

The coefficient of m gives the change in cost for each additional mile.

5. QuestionMultiple choice

A ticket model allows 0≤x≤1000\le x\le100 tickets. What is the meaningful domain?

Please select an answer first.

Correct answer: A

The correct answer is Whole-number ticket counts from 0 through 100..

  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 number of tickets must be a whole number within the stated capacity.
  3. Check the graph or value: The correct choice is Whole-number ticket counts from 0 through 100..

The number of tickets must be a whole number within the stated capacity.

6. QuestionMultiple choice

A population model is P=1200+50tP=1200+50t. What is the population at t = 3?

Please select an answer first.

Correct answer: B

The correct answer is 1350.

  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 t = 3: P = 1200 + 50(3) = 1350.
  3. Check the graph or value: The correct choice is 1350.

Substitute t = 3: P = 1200 + 50(3) = 1350.

7. QuestionMultiple choice

At what x-value do y=10x+20y=10x+20 and y=15xy=15x have the same output?

Please select an answer first.

Correct answer: C

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: Set the expressions equal: 10x + 20 = 15x, so 20 = 5x and x = 4.
  3. Check the graph or value: The correct choice is 4.

Set the expressions equal: 10x + 20 = 15x, so 20 = 5x and x = 4.

8. QuestionMultiple choice

If y=7xy=7x, what is y when x = 4?

Please select an answer first.

Correct answer: D

The correct answer is 28.

  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: Multiply 7 by 4 to get y = 28.
  3. Check the graph or value: The correct choice is 28.

Multiply 7 by 4 to get y = 28.

9. QuestionMultiple choice

If y=24xy=\frac{24}{x}, what is y when x = 6?

Please select an answer first.

Correct answer: A

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: Substitute x = 6: y = 24/6 = 4.
  3. Check the graph or value: The correct choice is 4.

Substitute x = 6: y = 24/6 = 4.

10. QuestionMultiple choice

What is the average rate of change from (2, 10) to (5, 25)?

Please select an answer first.

Correct answer: B

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: Compute (25 - 10)/(5 - 2) = 15/3 = 5.
  3. Check the graph or value: The correct choice is 5.

Compute (25 - 10)/(5 - 2) = 15/3 = 5.

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