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Functions and Graphs Practice Tests

These Grade 12 Math practice tests develop fluency with function notation, domains, ranges, intercepts, transformations, compositions, inverses, polynomial and rational graphs, radical functions, exponential and logarithmic models, and trigonometric graphs.

Skills covered

  • Evaluating functions and interpreting intercepts, slopes, rates of change, domains, and ranges
  • Recognizing translations, reflections, stretches, compressions, vertices, zeros, and end behavior
  • Analyzing polynomial, rational, radical, absolute-value, piecewise, exponential, and logarithmic graphs
  • Reading amplitude, period, midline, and asymptotes in trigonometric and logarithmic functions
  • Computing compositions, inverse functions, inverse points, and function models from data

How to use these practice tests

Start with the parent function or algebraic rule. Then identify the transformation, restriction, intercept, asymptote, or composition and verify the result with substitution or a graph feature.

For more Grade 12 Math practice, return to the Grade 12 Math category.

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5 Tests
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1. Test

Grade 12 Functions and Graphs Practice Tests

Practice Grade 12 Math questions about function notation, domains, ranges, transformations, polynomial, rational, radical, exponential, logarithmic, trigonometric, inverse, and composite graphs.

Choose the best answer. Read the rule or graph feature carefully, apply the relevant transformation or function property, and check domain and range restrictions.

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

If f(x)=3x−2f(x)=3x-2, what is f(5)?

Please select an answer first.

Correct answer: A

The correct answer is 13.

  1. Read the graph or function rule: Identify the input, output, transformation, intercept, interval, or function family described in the question.
  2. Apply the function relationship: Substitute x=5: f(5)=3(5)-2=13.
  3. Check the graph feature: The correct answer is 13.

Substitute x=5: f(5)=3(5)-2=13.

2. QuestionMultiple choice

What is the y-intercept of y=−4x+9y=-4x+9?

Please select an answer first.

Correct answer: B

The correct answer is 9.

  1. Read the graph or function rule: Identify the input, output, transformation, intercept, interval, or function family described in the question.
  2. Apply the function relationship: The y-intercept is the constant term, so the graph crosses the y-axis at (0,9).
  3. Check the graph feature: The correct answer is 9.

The y-intercept is the constant term, so the graph crosses the y-axis at (0,9).

3. QuestionMultiple choice

What is the domain of f(x)=1x+6f(x)=\frac{1}{x+6}?

Please select an answer first.

Correct answer: C

The correct answer is All real numbers except x=-6.

  1. Read the graph or function rule: Identify the input, output, transformation, intercept, interval, or function family described in the question.
  2. Apply the function relationship: The denominator cannot equal zero, so x+6≠0 and x≠-6.
  3. Check the graph feature: The correct answer is All real numbers except x=-6.

The denominator cannot equal zero, so x+6≠0 and x≠-6.

4. QuestionMultiple choice

Which equation represents a line with slope 2 passing through (1,5)?

Please select an answer first.

Correct answer: D

The correct answer is y=2x+3y=2x+3.

  1. Read the graph or function rule: Identify the input, output, transformation, intercept, interval, or function family described in the question.
  2. Apply the function relationship: Using y-5=2(x-1) gives y=2x+3.
  3. Check the graph feature: The correct answer is y=2x+3y=2x+3.

Using y-5=2(x-1) gives y=2x+3.

5. QuestionMultiple choice

What is the range of f(x)=x2+4f(x)=x^2+4?

Please select an answer first.

Correct answer: A

The correct answer is y≥4y\ge4.

  1. Read the graph or function rule: Identify the input, output, transformation, intercept, interval, or function family described in the question.
  2. Apply the function relationship: Since x^2≥0, the minimum output is 4.
  3. Check the graph feature: The correct answer is y≥4y\ge4.

Since x^2≥0, the minimum output is 4.

6. QuestionMultiple choice

What is the slope of the secant line for f(x)=x2f(x)=x^2 from x=1 to x=4?

Please select an answer first.

Correct answer: B

The correct answer is 5.

  1. Read the graph or function rule: Identify the input, output, transformation, intercept, interval, or function family described in the question.
  2. Apply the function relationship: The slope is (16-1)/(4-1)=15/3=5.
  3. Check the graph feature: The correct answer is 5.

The slope is (16-1)/(4-1)=15/3=5.

7. QuestionMultiple choice

Which equation is a function of x?

Please select an answer first.

Correct answer: C

The correct answer is y=x+1y=\sqrt{x+1}.

  1. Read the graph or function rule: Identify the input, output, transformation, intercept, interval, or function family described in the question.
  2. Apply the function relationship: For each allowed x, the principal square root gives one y-value.
  3. Check the graph feature: The correct answer is y=x+1y=\sqrt{x+1}.

For each allowed x, the principal square root gives one y-value.

8. QuestionMultiple choice

What is the zero of f(x)=5x+10f(x)=5x+10?

Please select an answer first.

Correct answer: D

The correct answer is x=−2x=-2.

  1. Read the graph or function rule: Identify the input, output, transformation, intercept, interval, or function family described in the question.
  2. Apply the function relationship: Set 5x+10=0 and solve x=-2.
  3. Check the graph feature: The correct answer is x=−2x=-2.

Set 5x+10=0 and solve x=-2.

9. QuestionMultiple choice

If f(x)=x−4f(x)=x-4, what is f−1(7)f^{-1}(7)?

Please select an answer first.

Correct answer: A

The correct answer is 11.

  1. Read the graph or function rule: Identify the input, output, transformation, intercept, interval, or function family described in the question.
  2. Apply the function relationship: The inverse is f^(-1)(x)=x+4, so f^(-1)(7)=11.
  3. Check the graph feature: The correct answer is 11.

The inverse is f^(-1)(x)=x+4, so f^(-1)(7)=11.

10. QuestionMultiple choice

What does a negative slope indicate on a linear graph?

Please select an answer first.

Correct answer: B

The correct answer is The output decreases as the input increases.

  1. Read the graph or function rule: Identify the input, output, transformation, intercept, interval, or function family described in the question.
  2. Apply the function relationship: A negative slope means y changes downward as x moves to the right.
  3. Check the graph feature: The correct answer is The output decreases as the input increases.

A negative slope means y changes downward as x moves to the right.

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