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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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1. Test

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)=2x+3f(x)=2x+3, what is f(4)?

Please select an answer first.

Correct answer: A

The correct answer is 11.

  1. Identify the precalculus structure: Determine the function type, domain, transformation, composition, inverse, asymptote, model, or trigonometric relationship involved.
  2. Apply the relationship: Substitute x=4: f(4)=2(4)+3=11.
  3. Check the result: The correct answer is 11.

Substitute x=4: f(4)=2(4)+3=11.

2. QuestionMultiple choice

What is the domain of f(x)=1x−5f(x)=\frac{1}{x-5}?

Please select an answer first.

Correct answer: B

The correct answer is All real numbers except x=5.

  1. Identify the precalculus structure: Determine the function type, domain, transformation, composition, inverse, asymptote, model, or trigonometric relationship involved.
  2. Apply the relationship: The denominator cannot be zero, so x-5≠0 and x≠5.
  3. Check the result: The correct answer is All real numbers except x=5.

The denominator cannot be zero, so x-5≠0 and x≠5.

3. QuestionMultiple choice

What is the range of y=x2y=x^2?

Please select an answer first.

Correct answer: C

The correct answer is y≥0y\ge0.

  1. Identify the precalculus structure: Determine the function type, domain, transformation, composition, inverse, asymptote, model, or trigonometric relationship involved.
  2. Apply the relationship: A square is never negative, and the minimum value is 0.
  3. Check the result: The correct answer is y≥0y\ge0.

A square is never negative, and the minimum value is 0.

4. QuestionMultiple choice

Which test determines whether a graph represents a function of x?

Please select an answer first.

Correct answer: D

The correct answer is The vertical line test.

  1. Identify the precalculus structure: Determine the function type, domain, transformation, composition, inverse, asymptote, model, or trigonometric relationship involved.
  2. Apply the relationship: A graph is a function of x when no vertical line intersects it more than once.
  3. Check the result: The correct answer is The vertical line test.

A graph is a function of x when no vertical line intersects it more than once.

5. QuestionMultiple choice

Which condition describes an even function?

Please select an answer first.

Correct answer: A

The correct answer is f(−x)=f(x)f(-x)=f(x).

  1. Identify the precalculus structure: Determine the function type, domain, transformation, composition, inverse, asymptote, model, or trigonometric relationship involved.
  2. Apply the relationship: Even functions are symmetric about the y-axis and satisfy f(-x)=f(x).
  3. Check the result: The correct answer is f(−x)=f(x)f(-x)=f(x).

Even functions are symmetric about the y-axis and satisfy f(-x)=f(x).

6. QuestionMultiple choice

Which condition describes an odd function?

Please select an answer first.

Correct answer: B

The correct answer is f(−x)=−f(x)f(-x)=-f(x).

  1. Identify the precalculus structure: Determine the function type, domain, transformation, composition, inverse, asymptote, model, or trigonometric relationship involved.
  2. Apply the relationship: Odd functions have origin symmetry and satisfy f(-x)=-f(x).
  3. Check the result: The correct answer is f(−x)=−f(x)f(-x)=-f(x).

Odd functions have origin symmetry and satisfy f(-x)=-f(x).

7. QuestionMultiple choice

What is the x-intercept of f(x)=3x−6f(x)=3x-6?

Please select an answer first.

Correct answer: C

The correct answer is 2.

  1. Identify the precalculus structure: Determine the function type, domain, transformation, composition, inverse, asymptote, model, or trigonometric relationship involved.
  2. Apply the relationship: Set f(x)=0: 3x-6=0, so x=2.
  3. Check the result: The correct answer is 2.

Set f(x)=0: 3x-6=0, so x=2.

8. QuestionMultiple choice

What is the average rate of change of f(x)=x2f(x)=x^2 from x=1 to x=3?

Please select an answer first.

Correct answer: D

The correct answer is 4.

  1. Identify the precalculus structure: Determine the function type, domain, transformation, composition, inverse, asymptote, model, or trigonometric relationship involved.
  2. Apply the relationship: Compute (f(3)-f(1))/(3-1)=(9-1)/2=4.
  3. Check the result: The correct answer is 4.

Compute (f(3)-f(1))/(3-1)=(9-1)/2=4.

9. QuestionMultiple choice

If f(x)=x+1f(x)=x+1 and g(x)=2xg(x)=2x, what is f(g(x))f(g(x))?

Please select an answer first.

Correct answer: A

The correct answer is 2x+12x+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)=2x into f: f(g(x))=2x+1.
  3. Check the result: The correct answer is 2x+12x+1.

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

10. QuestionMultiple choice

If f(x)=2x+1f(x)=2x+1, what is f(a+h)?

Please select an answer first.

Correct answer: B

The correct answer is 2a+2h+12a+2h+1.

  1. Identify the precalculus structure: Determine the function type, domain, transformation, composition, inverse, asymptote, model, or trigonometric relationship involved.
  2. Apply the relationship: Replace x with a+h: f(a+h)=2(a+h)+1=2a+2h+1.
  3. Check the result: The correct answer is 2a+2h+12a+2h+1.

Replace x with a+h: f(a+h)=2(a+h)+1=2a+2h+1.

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