Domain and Range Calculator

Enter a function of x to get its domain and range in interval notation — shown on a graph with the domain marked along the x-axis and the range along the y-axis.

Domain
Range

domain (on the x-axis)range (on the y-axis)

How to Find the Domain and Range

Enter a function of x and read its domain and range from the result and the graph.

1

Enter a function

Type a function of x, such as sqrt(x), 1/(x - 2) or . Functions like sqrt, ln, log and abs are supported.

2

Read the domain

The domain is every x-value the function accepts, in interval notation. Square roots exclude negatives, logs need a positive input, and fractions exclude values that make the denominator zero.

3

Read the range

The range is every y-value the function produces. On the graph, the domain is drawn along the x-axis and the range along the y-axis so you can see both at a glance.

Frequently Asked Questions

What is the domain of a function?
The domain is the set of all input values (x) for which the function is defined. For example, sqrt(x) has domain [0, ∞) because you cannot take the square root of a negative number, and 1/x has domain (−∞, 0) ∪ (0, ∞) because it is undefined at x = 0.
What is the range of a function?
The range is the set of all output values (y) the function can produce. For x², the range is [0, ∞) because a square is never negative; for sin(x) it is [−1, 1]; and for 1/x it is (−∞, 0) ∪ (0, ∞).
How is the domain and range written?
In interval notation. A round bracket ( or ) excludes an endpoint, a square bracket [ or ] includes it, ∞ marks an unbounded end, and ∪ joins separate pieces — so [0, ∞) means zero and every value above it.
How does the calculator work?
It samples the function across the real line to find where it is defined and which y-values it reaches, then reports both in interval notation. It handles the common textbook functions well; for unusual or piecewise functions, check the graph alongside the result.
Is my data sent anywhere?
No. Everything runs in your browser with JavaScript; nothing you type is uploaded or stored.