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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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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

What is the y-intercept of y=2x−3y=2^x-3?

Please select an answer first.

Correct answer: A

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: At x=0, y=2^0-3=1-3=-2.
  3. Check the graph feature: The correct answer is -2.

At x=0, y=2^0-3=1-3=-2.

2. QuestionMultiple choice

What is the range of y=3x+4y=3^x+4?

Please select an answer first.

Correct answer: B

The correct answer is y>4y>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: The exponential term is positive, so the graph approaches but never reaches y=4.
  3. Check the graph feature: The correct answer is y>4y>4.

The exponential term is positive, so the graph approaches but never reaches y=4.

3. QuestionMultiple choice

What is the vertical asymptote of y=log⁡2(x+5)y=\log_2(x+5)?

Please select an answer first.

Correct answer: C

The correct answer is x=−5x=-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 logarithm argument is zero at x=-5.
  3. Check the graph feature: The correct answer is x=−5x=-5.

The logarithm argument is zero at x=-5.

4. QuestionMultiple choice

How does y=2−xy=2^{-x} behave as x increases?

Please select an answer first.

Correct answer: D

The correct answer is It decreases toward zero.

  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 negative exponent creates exponential decay.
  3. Check the graph feature: The correct answer is It decreases toward zero.

The negative exponent creates exponential decay.

5. QuestionMultiple choice

What is the amplitude of y=3sin⁡x−1y=3\sin x-1?

Please select an answer first.

Correct answer: A

The correct answer is 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: Amplitude is the absolute value of the sine coefficient.
  3. Check the graph feature: The correct answer is 3.

Amplitude is the absolute value of the sine coefficient.

6. QuestionMultiple choice

What is the period of y=cos⁡(4x)y=\cos(4x)?

Please select an answer first.

Correct answer: B

The correct answer is π2\frac{\pi}{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 period is 2π/4=π/2.
  3. Check the graph feature: The correct answer is π2\frac{\pi}{2}.

The period is 2π/4=π/2.

7. QuestionMultiple choice

What is the range of y=2cos⁡x+1y=2\cos x+1?

Please select an answer first.

Correct answer: C

The correct answer is [−1,3][-1,3].

  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: Since -1≤cos x≤1, multiplying by 2 and adding 1 gives -1≤y≤3.
  3. Check the graph feature: The correct answer is [−1,3][-1,3].

Since -1≤cos x≤1, multiplying by 2 and adding 1 gives -1≤y≤3.

8. QuestionMultiple choice

Which graph has period π\pi?

Please select an answer first.

Correct answer: D

The correct answer is y=sin⁡(2x)y=\sin(2x).

  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 period of sin(Bx) is 2π/|B|; for B=2 it is π.
  3. Check the graph feature: The correct answer is y=sin⁡(2x)y=\sin(2x).

The period of sin(Bx) is 2π/|B|; for B=2 it is π.

9. QuestionMultiple choice

What is the inverse of y=10xy=10^x?

Please select an answer first.

Correct answer: A

The correct answer is y=log⁡xy=\log 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: The common logarithm is the inverse of the base-10 exponential function.
  3. Check the graph feature: The correct answer is y=log⁡xy=\log x.

The common logarithm is the inverse of the base-10 exponential function.

10. QuestionMultiple choice

What does the parameter k do in y=asin⁡(bx)+ky=a\sin(bx)+k?

Please select an answer first.

Correct answer: B

The correct answer is It shifts the graph vertically.

  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: Adding k outside the sine changes the midline and vertical position.
  3. Check the graph feature: The correct answer is It shifts the graph vertically.

Adding k outside the sine changes the midline and vertical position.

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