Domain and Range
A free College Algebra lesson from the “Functions” unit, with a worked example and practice problems including step-by-step solutions.
Domain is the set of allowed inputs, and range is the set of possible outputs. Restrictions may come from denominators, radicals, graphs, or real-world meaning.
What you'll learn
- Find domain and range from representations
- Identify restrictions
- Use context to limit domains
Worked example
Problem. For f(x) = 1/(x - 3), what value is excluded from the domain?
- The denominator cannot equal zero.
- x - 3 = 0 when x = 3.
- So x = 3 is excluded.
Answer: 3
Lesson preview: this page shows 5 practice items. The interactive activity contains 28 practice items and 15 quiz items (multiple choice and typed response). Counts include repeated prompts and variants.
Practice problems
1. For points (1, 5), (2, 8), and (4, 8), the range is...
Choices: {5, 8} · {1, 2, 4} · {1, 5} · {2, 4, 8}
Show solution
- Range uses output values.
Answer: {5, 8}
2. For f(x) = 1/(x + 9), what value is excluded?
Show solution
- x + 9 cannot be 0.
Answer: -9
3. For g(x) = sqrt(x - 7), what is the smallest allowed x-value?
Show solution
- x - 7 must be at least 0.
Answer: 7
4. For f(x) = 1/(x - 5), what value is excluded?
Show solution
- The denominator cannot be zero.
Answer: 5
5. For g(x) = sqrt(12 - x), what is the largest allowed x-value?
Show solution
- 12 - x must be at least 0.
Answer: 12
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