Domain and Range Calculator
Pick a function type below to instantly get its domain and range.
Domain
All real numbers
Range
y ≥ 0
Common Domain & Range Rules
- Linear and quadratic functions: domain is always all real numbers.
- Square root functions: domain is restricted to where the inside stays non-negative.
- Reciprocal functions: domain excludes wherever the denominator would be zero.
Worked example
f(x) = √(x − 3) + 2.
The expression under the root needs x − 3 ≥ 0, so x ≥ 3.
Domain: x ≥ 3. Range: y ≥ 2.
Frequently Asked Questions
What is the domain of a function?
The domain is every input (x-value) the function can accept without breaking a math rule, like dividing by zero or taking the square root of a negative number.
What is the range of a function?
The range is every possible output (y-value) the function can actually produce.
Why does a square root function have a restricted domain?
The square root of a negative number isn't a real number, so a square root function's domain only includes inputs that keep the expression under the radical at zero or above.
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