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Precalculus Introduction Practice Tests

These Grade 11 Math practice tests connect core function ideas before advanced calculus study, including notation, domains, ranges, compositions, inverses, transformations, polynomial and rational behavior, exponential and logarithmic relationships, trigonometry, and modeling.

Skills covered

  • Evaluating functions, average rates of change, domains, ranges, and symmetry
  • Computing compositions and inverses and interpreting graph transformations
  • Analyzing polynomial zeros, end behavior, rational domains, holes, and asymptotes
  • Connecting exponential, logarithmic, and trigonometric functions
  • Using piecewise, absolute-value, quadratic, radical, and proportional models

How to use these practice tests

Identify the function family first, write domain restrictions, choose the form that exposes the needed feature, and verify compositions, inverses, transformations, and model outputs.

For more Grade 11 Math practice, return to the Grade 11 Math category.

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Grade 11 Precalculus Introduction Practice Tests

Practice Grade 11 Math questions about functions, domains, ranges, composition, inverses, transformations, polynomial and rational functions, exponential and logarithmic models, and trigonometry.

Choose the best answer. Identify the function structure, apply the appropriate algebraic or trigonometric relationship, and check domains and model assumptions.

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

If f(x)=x2f(x)=x^2 and g(x)=x+3g(x)=x+3, what is f(g(x))f(g(x))?

Please select an answer first.

Correct answer: A

The correct answer is (x+3)2(x+3)^2.

  1. Identify the precalculus structure: Determine the function type, domain, transformation, composition, inverse, asymptote, model, or trigonometric relationship involved.
  2. Apply the relationship: Substitute g(x)=x+3 into f(x)=x^2.
  3. Check the result: The correct answer is (x+3)2(x+3)^2.

Substitute g(x)=x+3 into f(x)=x^2.

2. QuestionMultiple choice

If f(x)=x2f(x)=x^2 and g(x)=x+3g(x)=x+3, what is g(f(x))g(f(x))?

Please select an answer first.

Correct answer: B

The correct answer is x2+3x^2+3.

  1. Identify the precalculus structure: Determine the function type, domain, transformation, composition, inverse, asymptote, model, or trigonometric relationship involved.
  2. Apply the relationship: Substitute f(x)=x^2 into g(x)=x+3.
  3. Check the result: The correct answer is x2+3x^2+3.

Substitute f(x)=x^2 into g(x)=x+3.

3. QuestionMultiple choice

What is the inverse of f(x)=2x−5f(x)=2x-5?

Please select an answer first.

Correct answer: C

The correct answer is f−1(x)=x+52f^{-1}(x)=\frac{x+5}{2}.

  1. Identify the precalculus structure: Determine the function type, domain, transformation, composition, inverse, asymptote, model, or trigonometric relationship involved.
  2. Apply the relationship: Let y=2x-5, swap x and y, then solve x=2y-5 for y=(x+5)/2.
  3. Check the result: The correct answer is f−1(x)=x+52f^{-1}(x)=\frac{x+5}{2}.

Let y=2x-5, swap x and y, then solve x=2y-5 for y=(x+5)/2.

4. QuestionMultiple choice

What is the domain of f(x)=x−4f(x)=\sqrt{x-4}?

Please select an answer first.

Correct answer: D

The correct answer is x≥4x\ge4.

  1. Identify the precalculus structure: Determine the function type, domain, transformation, composition, inverse, asymptote, model, or trigonometric relationship involved.
  2. Apply the relationship: The radicand must be nonnegative: x-4≥0, so x≥4.
  3. Check the result: The correct answer is x≥4x\ge4.

The radicand must be nonnegative: x-4≥0, so x≥4.

5. QuestionMultiple choice

How is y=∣x−2∣+3y=|x-2|+3 transformed from y=∣x∣y=|x|?

Please select an answer first.

Correct answer: A

The correct answer is Shift right 2 and up 3..

  1. Identify the precalculus structure: Determine the function type, domain, transformation, composition, inverse, asymptote, model, or trigonometric relationship involved.
  2. Apply the relationship: Replacing x with x-2 shifts right 2, and adding 3 shifts up 3.
  3. Check the result: The correct answer is Shift right 2 and up 3..

Replacing x with x-2 shifts right 2, and adding 3 shifts up 3.

6. QuestionMultiple choice

What geometric transformation represents the graph of an inverse function?

Please select an answer first.

Correct answer: B

The correct answer is Reflection across y=x.

  1. Identify the precalculus structure: Determine the function type, domain, transformation, composition, inverse, asymptote, model, or trigonometric relationship involved.
  2. Apply the relationship: A function and its inverse exchange x and y, producing reflection across y=x.
  3. Check the result: The correct answer is Reflection across y=x.

A function and its inverse exchange x and y, producing reflection across y=x.

7. QuestionMultiple choice

If f(x)=x+2f(x)=x+2 and g(x)=3x−1g(x)=3x-1, what is f(g(x))f(g(x))?

Please select an answer first.

Correct answer: C

The correct answer is 3x+13x+1.

  1. Identify the precalculus structure: Determine the function type, domain, transformation, composition, inverse, asymptote, model, or trigonometric relationship involved.
  2. Apply the relationship: Substitute g(x) into f: f(g(x))=(3x-1)+2=3x+1.
  3. Check the result: The correct answer is 3x+13x+1.

Substitute g(x) into f: f(g(x))=(3x-1)+2=3x+1.

8. QuestionMultiple choice

When does a function have an inverse function?

Please select an answer first.

Correct answer: D

The correct answer is When it is one-to-one on its domain..

  1. Identify the precalculus structure: Determine the function type, domain, transformation, composition, inverse, asymptote, model, or trigonometric relationship involved.
  2. Apply the relationship: A one-to-one function passes the horizontal line test, allowing each output to have one input.
  3. Check the result: The correct answer is When it is one-to-one on its domain..

A one-to-one function passes the horizontal line test, allowing each output to have one input.

9. QuestionMultiple choice

What is the inverse of f(x)=x3f(x)=x^3?

Please select an answer first.

Correct answer: A

The correct answer is f−1(x)=x3f^{-1}(x)=\sqrt[3]{x}.

  1. Identify the precalculus structure: Determine the function type, domain, transformation, composition, inverse, asymptote, model, or trigonometric relationship involved.
  2. Apply the relationship: Swap x and y in y=x^3 and solve: y=cube root of x.
  3. Check the result: The correct answer is f−1(x)=x3f^{-1}(x)=\sqrt[3]{x}.

Swap x and y in y=x^3 and solve: y=cube root of x.

10. QuestionMultiple choice

What transformation changes f(x) into -f(x)?

Please select an answer first.

Correct answer: B

The correct answer is Reflection across the x-axis.

  1. Identify the precalculus structure: Determine the function type, domain, transformation, composition, inverse, asymptote, model, or trigonometric relationship involved.
  2. Apply the relationship: Multiplying output values by -1 reflects the graph over the x-axis.
  3. Check the result: The correct answer is Reflection across the x-axis.

Multiplying output values by -1 reflects the graph over the x-axis.

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