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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. 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)=x+3f(x)=x+3 and g(x)=2xg(x)=2x, what is f(g(4))f(g(4))?

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: g(4)=8, then f(8)=8+3=11.
  3. Check the graph feature: The correct answer is 11.

g(4)=8, then f(8)=8+3=11.

2. QuestionMultiple choice

If f(x)=2x−1f(x)=2x-1, what is f−1(x)f^{-1}(x)?

Please select an answer first.

Correct answer: B

The correct answer is x+12\frac{x+1}{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: Swap x and y in y=2x-1 and solve y=(x+1)/2.
  3. Check the graph feature: The correct answer is x+12\frac{x+1}{2}.

Swap x and y in y=2x-1 and solve y=(x+1)/2.

3. QuestionMultiple choice

What condition ensures that a function has an inverse function on its domain?

Please select an answer first.

Correct answer: C

The correct answer is It is one-to-one.

  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 one-to-one function gives each output exactly one input.
  3. Check the graph feature: The correct answer is It is one-to-one.

A one-to-one function gives each output exactly one input.

4. QuestionMultiple choice

What is (f∘f)(x)(f\circ f)(x) if f(x)=x+2f(x)=x+2?

Please select an answer first.

Correct answer: D

The correct answer is x+4x+4.

  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: Apply f twice: f(f(x))=(x+2)+2=x+4.
  3. Check the graph feature: The correct answer is x+4x+4.

Apply f twice: f(f(x))=(x+2)+2=x+4.

5. QuestionMultiple choice

What does the inverse graph of a one-to-one function reflect across?

Please select an answer first.

Correct answer: A

The correct answer is The line y=xy=x.

  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: Swapping inputs and outputs reflects points across y=x.
  3. Check the graph feature: The correct answer is The line y=xy=x.

Swapping inputs and outputs reflects points across y=x.

6. QuestionMultiple choice

If a graph passes through (2,7), which point lies on the inverse graph?

Please select an answer first.

Correct answer: B

The correct answer is (7,2).

  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: The inverse exchanges the coordinates of every point.
  3. Check the graph feature: The correct answer is (7,2).

The inverse exchanges the coordinates of every point.

7. QuestionMultiple choice

What is the average rate of change of a function represented by the points (1,4) and (5,12)?

Please select an answer first.

Correct answer: C

The correct answer is 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: The slope is (12-4)/(5-1)=8/4=2.
  3. Check the graph feature: The correct answer is 2.

The slope is (12-4)/(5-1)=8/4=2.

8. QuestionMultiple choice

A function has a constant second difference in a table. What type of model is appropriate?

Please select an answer first.

Correct answer: D

The correct answer is Quadratic.

  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: Constant second differences indicate a quadratic relationship.
  3. Check the graph feature: The correct answer is Quadratic.

Constant second differences indicate a quadratic relationship.

9. QuestionMultiple choice

Which model represents a quantity that doubles every time x increases by 1?

Please select an answer first.

Correct answer: A

The correct answer is An exponential model.

  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: Repeated multiplication by 2 is exponential behavior.
  3. Check the graph feature: The correct answer is An exponential model.

Repeated multiplication by 2 is exponential behavior.

10. QuestionMultiple choice

What does the intersection of two function graphs represent?

Please select an answer first.

Correct answer: B

The correct answer is An input-output pair where the functions have equal values.

  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: At an intersection, both functions produce the same y-value for the same x-value.
  3. Check the graph feature: The correct answer is An input-output pair where the functions have equal values.

At an intersection, both functions produce the same y-value for the same x-value.

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