Determine domain and range from equations, graphs, or context.
Domain is the allowed inputs, and range is the outputs the function can produce.
Core Idea
The domain is the set of allowed inputs. The range is the set of resulting outputs. Use the equation, graph, or context to spot restrictions before you start calculating.
Understanding
Rule: ACT questions often hide domain restrictions in radicals, denominators, graphs with endpoints, or real-world limits. For a radical, the expression inside must be nonnegative. For a rational expression, the denominator cannot be zero. For a context, time, length, and counts may also narrow the domain.
Range comes after that: once you know which inputs are possible, ask what outputs the rule can produce. On graphs, domain is read left to right, and range is read bottom to top. Closed dots include values; open dots exclude them.
Step by Step
- Check the formula for built-in restrictions such as radicals and denominators.
- If a graph is given, read domain from left to right and range from bottom to top.
- If the problem is contextual, remove impossible inputs such as negative time or fractional counts when they do not make sense.
- State the answer as a set or inequality, not just a verbal guess.
Worked Example
What is the domain of
Select an answer to see the explanation