Domain and Range
Domain is all allowed inputs; range is all outputs.
Key idea
Domain is all allowed inputs; range is all outputs.
In depth
The domain is the set of allowed inputs and the range is the set of outputs. Restrictions come from division by zero and negative values under even roots.
Worked example
f(x) = √(x − 2) has domain x ≥ 2 and range y ≥ 0.
Real-world uses
- Deciding which inputs make sense for time, length or counts
- Checking valid outputs in models
Common mistake
Confusing domain with range, or forgetting to exclude values that make denominators zero.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Domain and Range?
Domain is all allowed inputs; range is all outputs. It is a topic at the intermediate level in Algebra.
Where is Domain and Range used in real life?
Real-world examples: Deciding which inputs make sense for time, length or counts; Checking valid outputs in models.
What should I learn before Domain and Range?
Make sure you are comfortable with Function Notation, the previous topic in Algebra.
What is a common mistake with Domain and Range?
Confusing domain with range, or forgetting to exclude values that make denominators zero.
How can I practise Domain and Range?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Domain and Range?
Move on to Relations vs Functions next.
Related intermediate topics in Algebra
- Multi-Step Equations – Distribute, combine like terms, move variables to one side.
- Variables on Both Sides – Collect variable terms on one side first.
- Literal Equations – Rearrange formulas to solve for a chosen variable.
- Identity and No-Solution Equations – Some equations are always true or never true.
- Linear Inequalities – Solve like equations but reverse the sign when multiplying by a negative.
- Compound Inequalities – Combine two inequalities using “and” or “or”.