How to Find the Domain and Range of a Function
The domain is the set of all x-values a function can accept, and the range is the set of all y-values it can produce. Three things can break a domain: division by zero, an even root of a negative number, and a logarithm of a non-positive number. Check for those three first, and most domain problems solve themselves.
Interval Notation Basics
- Parentheses ( ) exclude an endpoint: (2, 5) means 2 < x < 5.
- Brackets [ ] include an endpoint: [0, โ) means x โฅ 0.
- Infinity always gets a parenthesis: (โโ, โ) is the whole real line.
Range Strategies
For a parabola, complete the square to find the vertex โ the range starts or ends there. For 1/x style rational functions, the range is everything except the horizontal asymptote value. When in doubt, sketch the graph: the range is simply how far the curve stretches vertically.
Working with equations? Try our linear equation solver or the derivative calculator to locate maxima and minima.