Domain and Range
A free Algebra II lesson from the “Functions and Notation” unit, with a worked example and practice problems including step-by-step solutions.
The domain is the set of allowed inputs. The range is the set of possible outputs. Restrictions can come from context, square roots, denominators, or a graph.
What you'll learn
- Identify domain and range
- Interpret restrictions
- Use interval and set descriptions
Worked example
Problem. A function is defined by the points (1, 5), (3, 7), and (6, 7). What is the range?
- The range is the set of y-values.
- The y-values are 5, 7, and 7.
- List repeats once: {5, 7}.
Answer: {5, 7}
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 (2, 8), (4, 9), and (6, 8), the domain is...
Choices: {2, 4, 6} · {8, 9} · {2, 8} · {4, 8, 9}
Show solution
- Domain uses x-values.
Answer: {2, 4, 6}
2. For points (2, 8), (4, 9), and (6, 8), the range is...
Choices: {8, 9} · {2, 4, 6} · {2, 8} · {4, 6}
Show solution
- Range uses y-values and removes repeats.
Answer: {8, 9}
3. For f(x) = 1/(x - 5), what value is excluded from the domain?
Show solution
- The denominator cannot be zero.
- x - 5 = 0 when x = 5.
Answer: 5
4. For g(x) = sqrt(x - 3), what is the smallest allowed x-value?
Show solution
- The expression under the square root must be at least 0.
Answer: 3
5. A movie ticket price function uses number of tickets as the input. Which domain makes sense?
Choices: Whole numbers 0 or greater · All real numbers · Only negative numbers · Only decimals between 0 and 1
Show solution
- You cannot buy a negative or fractional number of tickets.
Answer: Whole numbers 0 or greater
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