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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

How does y=(x−4)2+1y=(x-4)^2+1 compare with y=x2y=x^2?

Please select an answer first.

Correct answer: A

The correct answer is It shifts right 4 and up 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: The vertex moves from (0,0) to (4,1).
  3. Check the graph feature: The correct answer is It shifts right 4 and up 1.

The vertex moves from (0,0) to (4,1).

2. QuestionMultiple choice

What is the vertex of y=−2(x+3)2+5y=-2(x+3)^2+5?

Please select an answer first.

Correct answer: B

The correct answer is (−3,5)(-3,5).

  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: Vertex form y=a(x-h)^2+k has h=-3 and k=5.
  3. Check the graph feature: The correct answer is (−3,5)(-3,5).

Vertex form y=a(x-h)^2+k has h=-3 and k=5.

3. QuestionMultiple choice

What is the axis of symmetry of y=x2−8x+3y=x^2-8x+3?

Please select an answer first.

Correct answer: C

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: The axis is x=-b/(2a)=8/2=4.
  3. Check the graph feature: The correct answer is x=4x=4.

The axis is x=-b/(2a)=8/2=4.

4. QuestionMultiple choice

What is the maximum value of y=−x2+6x−2y=-x^2+6x-2?

Please select an answer first.

Correct answer: D

The correct answer is 7.

  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 vertex is at x=3, and y=-(3)^2+18-2=7.
  3. Check the graph feature: The correct answer is 7.

The vertex is at x=3, and y=-(3)^2+18-2=7.

5. QuestionMultiple choice

What is the end behavior of f(x)=x4−2x2f(x)=x^4-2x^2?

Please select an answer first.

Correct answer: A

The correct answer is Both ends rise to positive infinity.

  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: An even-degree polynomial with a positive leading coefficient rises on both ends.
  3. Check the graph feature: The correct answer is Both ends rise to positive infinity.

An even-degree polynomial with a positive leading coefficient rises on both ends.

6. QuestionMultiple choice

What are the x-intercepts of y=(x−1)(x+4)y=(x-1)(x+4)?

Please select an answer first.

Correct answer: B

The correct answer is x=1 and x=-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: Set each factor equal to zero.
  3. Check the graph feature: The correct answer is x=1 and x=-4.

Set each factor equal to zero.

7. QuestionMultiple choice

What is the multiplicity of x=2 in f(x)=(x−2)2(x+1)f(x)=(x-2)^2(x+1)?

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 factor x-2 is raised to the second power.
  3. Check the graph feature: The correct answer is 2.

The factor x-2 is raised to the second power.

8. QuestionMultiple choice

What happens at a zero with odd multiplicity for a polynomial graph?

Please select an answer first.

Correct answer: D

The correct answer is The graph crosses the x-axis.

  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: Odd multiplicity causes a sign change, so the graph crosses the axis at that zero.
  3. Check the graph feature: The correct answer is The graph crosses the x-axis.

Odd multiplicity causes a sign change, so the graph crosses the axis at that zero.

9. QuestionMultiple choice

Which parent function has a V-shaped graph?

Please select an answer first.

Correct answer: A

The correct answer is y=∣x∣y=|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 absolute-value parent function forms two line segments meeting at a vertex.
  3. Check the graph feature: The correct answer is y=∣x∣y=|x|.

The absolute-value parent function forms two line segments meeting at a vertex.

10. QuestionMultiple choice

What is the range of y=−∣x−2∣+6y=-|x-2|+6?

Please select an answer first.

Correct answer: B

The correct answer is y≤6y\le6.

  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 absolute value has a maximum of 6 at x=2.
  3. Check the graph feature: The correct answer is y≤6y\le6.

The negative absolute value has a maximum of 6 at x=2.

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