A domain and range calculator finds all possible inputs (the domain) and outputs (the range) of a function, and writes them in interval notation. It’s a core skill in algebra and precalculus, and step-by-step explanations help you understand why certain values are excluded.
To find the domain, look for values that break the function. For rational functions, exclude values that make the denominator zero: f(x) = 1/(x − 3) has domain (−∞, 3) ∪ (3, ∞). For square roots, the inside must be zero or positive: f(x) = √(x + 2) has domain [−2, ∞). For logarithms, the inside must be positive: f(x) = ln(x − 1) has domain (1, ∞). Polynomials have a domain of all real numbers.
Finding the range is often harder. Think about what outputs are possible. f(x) = x² has range [0, ∞), since squares are never negative. f(x) = √(x + 2) has range [0, ∞). For f(x) = 1/(x − 3), the output can be any real number except 0, so the range is (−∞, 0) ∪ (0, ∞). Graphing the function is a great way to see the range.
Interval notation tips: use brackets [ ] when an endpoint is included and parentheses ( ) when it isn’t, and always use parentheses with infinity. Use ∪ to join separate intervals.
Tips for getting accurate results from the Domain and Range Calculator: double-check that every input uses the right units, enter numbers without commas or symbols, and run the calculation a second time with a quick estimate in your head to confirm the answer looks reasonable.
How to use the Domain and Range Calculator on Minedit: enter your values in the fields, press calculate, and review the step-by-step breakdown under the result. If something looks off, change one input at a time to see how it affects the answer, which is also a great way to learn the math behind it.
Learn more on Wikipedia’s domain of a function article. Find end behavior, limit and axis of symmetry calculators on Minedit.