Domain and Range Calculator

This domain and range calculator gives the domain and range of several standard function types: linear, quadratic, square root and reciprocal. Choose the type and enter its parameters, and the calculator states the set of allowed inputs (the domain) and the set of possible outputs (the range). The domain is limited whenever a function would divide by zero or take the square root of a negative number, while the range depends on the shape of the graph, such as the turning point of a parabola. Reading off domain and range is a core skill in studying functions. The rules, a worked example and the assumptions are below.

Function type

a or m

c or h

Range

Function type

The formula

Linear mx + b: domain all reals, range all reals. Quadratic ax^2 + bx + c: domain all reals, range y at least k (a positive) or at most k (a negative), where k = c minus b^2/(4a). Square root of (x minus h): domain x at least h, range y at least 0. Reciprocal 1/(x minus h): domain x not equal to h, range y not equal to 0.

Worked example

For the quadratic x^2 minus 4x + 3 (a = 1, b = minus 4, c = 3), the vertex value is k = 3 minus 4 = minus 1, so the domain is all real numbers and the range is y greater than or equal to minus 1. Choose Quadratic and enter 1, -4, 3.

Frequently asked questions

What is the domain of a function?

The set of all input values for which the function is defined.

What is the range?

The set of all output values the function actually produces.

Why is the domain sometimes restricted?

To avoid dividing by zero or taking the square root of a negative number, which are undefined for real numbers.

Who this calculator is for

This calculator is for algebra students and anyone needing a quick, reliable result.

What this calculator assumes

You enter valid numbers.
The standard method is applied.
Results are rounded for display.

Formula and sources

Related calculators

Quadratic Formula Calculator: solve a quadratic.
Scientific Calculator: general maths.
Matrix Calculator: matrix operations.

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