What this calculator does
The domain of a function is every input (x-value) that produces a valid output, and the range is every possible output (y-value) the function can produce. This calculator covers seven common function families – linear, quadratic, square root, reciprocal, absolute value, exponential, and logarithmic – and applies the standard algebraic rule for each one.
How it works
Each family is written in a shifted form, such as y = a·√(x-h) + k, using the coefficient a and the shifts h and k you enter. For example, a square root function is only defined once the value under the root is zero or positive, so its domain starts at x = h. A reciprocal function is undefined wherever its denominator is zero, so x = h is excluded from its domain.
- Most polynomial-type functions (linear, quadratic, absolute value) have a domain of all real numbers.
- The sign of a flips whether a bounded range opens upward or downward.
This tool is for general math learning and reference purposes and assumes the standard, simplified form of each function family shown above.