NumicornNumicornLearn, solve, progress

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.

Select a test

5 Tests
1. Test2. Test3. Test4. Test5. Test

3. 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

What is the end behavior of f(x)=−2x4+3x2−1f(x)=-2x^4+3x^2-1?

Please select an answer first.

Correct answer: A

The correct answer is Both ends decrease toward negative infinity..

  1. Identify the precalculus structure: Determine the function type, domain, transformation, composition, inverse, asymptote, model, or trigonometric relationship involved.
  2. Apply the relationship: An even-degree polynomial with negative leading coefficient decreases on both ends.
  3. Check the result: The correct answer is Both ends decrease toward negative infinity..

An even-degree polynomial with negative leading coefficient decreases on both ends.

2. QuestionMultiple choice

What is the end behavior of a cubic polynomial with positive leading coefficient?

Please select an answer first.

Correct answer: B

The correct answer is Left end down and right end up.

  1. Identify the precalculus structure: Determine the function type, domain, transformation, composition, inverse, asymptote, model, or trigonometric relationship involved.
  2. Apply the relationship: An odd-degree polynomial with positive leading coefficient falls left and rises right.
  3. Check the result: The correct answer is Left end down and right end up.

An odd-degree polynomial with positive leading coefficient falls left and rises right.

3. QuestionMultiple choice

What are the zeros of 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 and -1.

  1. Identify the precalculus structure: Determine the function type, domain, transformation, composition, inverse, asymptote, model, or trigonometric relationship involved.
  2. Apply the relationship: Set the factors equal to zero: x=2 or x=-1.
  3. Check the result: The correct answer is 2 and -1.

Set the factors equal to zero: x=2 or x=-1.

4. QuestionMultiple choice

What is the multiplicity of the zero x=3 in (x−3)4(x+1)(x-3)^4(x+1)?

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: The exponent on the factor x-3 is 4, so its zero has multiplicity 4.
  3. Check the result: The correct answer is 4.

The exponent on the factor x-3 is 4, so its zero has multiplicity 4.

5. QuestionMultiple choice

What is the domain of f(x)=x+1x+2f(x)=\frac{x+1}{x+2}?

Please select an answer first.

Correct answer: A

The correct answer is All real numbers except x=-2.

  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 x+2 cannot be zero, so x=-2 is excluded.
  3. Check the result: The correct answer is All real numbers except x=-2.

The denominator x+2 cannot be zero, so x=-2 is excluded.

6. QuestionMultiple choice

What is the horizontal asymptote of f(x)=3x2+12x2−5f(x)=\frac{3x^2+1}{2x^2-5}?

Please select an answer first.

Correct answer: B

The correct answer is y=32y=\frac{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: Equal degrees give the ratio of leading coefficients, 3/2.
  3. Check the result: The correct answer is y=32y=\frac{3}{2}.

Equal degrees give the ratio of leading coefficients, 3/2.

7. QuestionMultiple choice

What graphical feature can result from a canceled common factor in a rational function?

Please select an answer first.

Correct answer: C

The correct answer is A hole.

  1. Identify the precalculus structure: Determine the function type, domain, transformation, composition, inverse, asymptote, model, or trigonometric relationship involved.
  2. Apply the relationship: Canceling a factor can remove one input from the original domain, creating a removable discontinuity or hole.
  3. Check the result: The correct answer is A hole.

Canceling a factor can remove one input from the original domain, creating a removable discontinuity or hole.

8. QuestionMultiple choice

If x-2 is a factor of polynomial p(x), what is p(2)?

Please select an answer first.

Correct answer: D

The correct answer is 0.

  1. Identify the precalculus structure: Determine the function type, domain, transformation, composition, inverse, asymptote, model, or trigonometric relationship involved.
  2. Apply the relationship: The Factor Theorem states that x-2 is a factor exactly when p(2)=0.
  3. Check the result: The correct answer is 0.

The Factor Theorem states that x-2 is a factor exactly when p(2)=0.

9. QuestionMultiple choice

What is a factorization of x3−8x^3-8?

Please select an answer first.

Correct answer: A

The correct answer is (x−2)(x2+2x+4)(x-2)(x^2+2x+4).

  1. Identify the precalculus structure: Determine the function type, domain, transformation, composition, inverse, asymptote, model, or trigonometric relationship involved.
  2. Apply the relationship: Use the difference-of-cubes formula a^3-b^3=(a-b)(a^2+ab+b^2).
  3. Check the result: The correct answer is (x−2)(x2+2x+4)(x-2)(x^2+2x+4).

Use the difference-of-cubes formula a^3-b^3=(a-b)(a^2+ab+b^2).

10. QuestionMultiple choice

What is the vertical asymptote of f(x)=x+1x−3f(x)=\frac{x+1}{x-3}?

Please select an answer first.

Correct answer: B

The correct answer is x=3x=3.

  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 is zero at x=3 and no common factor cancels.
  3. Check the result: The correct answer is x=3x=3.

The denominator is zero at x=3 and no common factor cancels.

Previous testNext test