Domain and Range Calculator

This calculator works out the domain and range of four standard function types: linear (mx + b), quadratic (ax^2 + bx + c), square root (the root of x minus h), and reciprocal (1 divided by x minus h). Domain and range are a core algebra concept: the domain is which input values a function accepts, the range is which output values it actually produces, and together they explain why some functions are undefined at certain points. Choose the function type from the dropdown, then enter its parameters, a or m for the leading coefficient, b, and c or h depending on the type selected. The calculator instantly returns the domain as the main result, along with the range and the function type chosen. For a quadratic, it works out the turning point so the range reflects whether the parabola opens upward or downward. For a square root function, the domain is restricted to values that keep the expression under the root from going negative, and for a reciprocal function both domain and range exclude the single value that would otherwise divide by zero. Use it to check homework answers, build intuition for how a function's shape limits its domain and range, or confirm a result quickly before a test. Try the default quadratic example, then switch the type and adjust the parameters to see how the results change.

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Function type

a or m

c or h

Domain: all real numbers

Rangeall real numbers

Function typelinear

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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