Excluded Values Practice Test

Find every input that makes an original denominator zero or a rational divisor invalid.

Excluded Values Practice Test

20 domain-restriction questions with worked explanations.

About This Excluded Values Practice Test

Excluded values are inputs for which an original rational expression is undefined. They come from denominator zeros and remain excluded even when a factor later cancels during simplification.

This test includes linear, quadratic, repeated, and fully factored denominators; expressions with several fractions; simplified expressions with retained restrictions; and rational expressions used as divisors.

Skills Covered

You will factor denominators, solve zero-factor equations, combine restrictions from several fractions, retain canceled exclusions, recognize denominators with no real zeros, and exclude zeros of a divisor.

How to Approach the Questions

  1. Inspect every denominator in the original unsimplified expression.
  2. Factor polynomial denominators completely.
  3. Set each denominator factor equal to zero.
  4. When dividing by a rational expression, also exclude values that make the divisor zero.

Common Mistakes to Avoid

Common errors include using numerator zeros, reversing signs in linear factors, forgetting one denominator in a sum, dropping restrictions after cancellation, assuming every quadratic has real zeros, and checking only where a divisor is undefined but not where it equals zero.

Practice Format

Use this free 20-question test for classroom review, tutoring, homework support, exam preparation, or independent practice. Each response is followed by an explanation, and the test can be repeated without registration.