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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 vertical asymptote of f(x)=3x−2f(x)=\frac{3}{x-2}?

Please select an answer first.

Correct answer: A

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: The denominator is zero at x=2.
  3. Check the graph feature: The correct answer is x=2x=2.

The denominator is zero at x=2.

2. QuestionMultiple choice

What is the horizontal asymptote of f(x)=2x+1x−4f(x)=\frac{2x+1}{x-4}?

Please select an answer first.

Correct answer: B

The correct answer is y=2y=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: Equal degrees give the ratio of leading coefficients, 2/1=2.
  3. Check the graph feature: The correct answer is y=2y=2.

Equal degrees give the ratio of leading coefficients, 2/1=2.

3. QuestionMultiple choice

What is the domain of f(x)=5−xf(x)=\sqrt{5-x}?

Please select an answer first.

Correct answer: C

The correct answer is x≤5x\le5.

  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 radicand must satisfy 5-x≥0, so x≤5.
  3. Check the graph feature: The correct answer is x≤5x\le5.

The radicand must satisfy 5-x≥0, so x≤5.

4. QuestionMultiple choice

What graphical feature does y=x−3+2y=\sqrt{x-3}+2 have at its starting point?

Please select an answer first.

Correct answer: D

The correct answer is Endpoint at (3,2).

  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 parent square-root graph starts at (0,0), then shifts right 3 and up 2.
  3. Check the graph feature: The correct answer is Endpoint at (3,2).

The parent square-root graph starts at (0,0), then shifts right 3 and up 2.

5. QuestionMultiple choice

If f(x)=∣x∣f(x)=|x|, what is f(−7)f(-7)?

Please select an answer first.

Correct answer: A

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: Absolute value gives the distance from zero, so |-7|=7.
  3. Check the graph feature: The correct answer is 7.

Absolute value gives the distance from zero, so |-7|=7.

6. QuestionMultiple choice

For the piecewise function f(x)=x+2f(x)=x+2 when x<1 and f(x)=x2f(x)=x^2 when x≥1, what is f(1)?

Please select an answer first.

Correct answer: B

The correct answer is 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: Because 1≥1, use the second rule: f(1)=1^2=1.
  3. Check the graph feature: The correct answer is 1.

Because 1≥1, use the second rule: f(1)=1^2=1.

7. QuestionMultiple choice

What does a hole in a rational graph represent?

Please select an answer first.

Correct answer: C

The correct answer is A removable discontinuity.

  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 canceled factor leaves one excluded input, shown as an open point.
  3. Check the graph feature: The correct answer is A removable discontinuity.

A canceled factor leaves one excluded input, shown as an open point.

8. QuestionMultiple choice

What is the oblique asymptote of f(x)=x2+2x+3x+1f(x)=\frac{x^2+2x+3}{x+1}?

Please select an answer first.

Correct answer: D

The correct answer is y=x+1y=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: Division gives x^2+2x+3=(x+1)(x+1)+2, so the quotient is y=x+1.
  3. Check the graph feature: The correct answer is y=x+1y=x+1.

Division gives x^2+2x+3=(x+1)(x+1)+2, so the quotient is y=x+1.

9. QuestionMultiple choice

Which transformation changes f(x)f(x) to f(x)+5f(x)+5?

Please select an answer first.

Correct answer: A

The correct answer is Shift the graph up 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: Adding outside the function changes every output by 5.
  3. Check the graph feature: The correct answer is Shift the graph up 5.

Adding outside the function changes every output by 5.

10. QuestionMultiple choice

Which transformation changes f(x)f(x) to f(x−2)f(x-2)?

Please select an answer first.

Correct answer: B

The correct answer is Shift the graph right 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: Replacing x with x-2 shifts the graph horizontally to the right.
  3. Check the graph feature: The correct answer is Shift the graph right 2.

Replacing x with x-2 shifts the graph horizontally to the right.

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