Math Functions Range


Given its domain, the range of a function is the set of all values to which a function is defined.



The range is the set of all possible outputs, which are calculated with the inputs of the domain.

As with the domain there are two possible notations:

  • Set notation
  • Interval notation


Following function is given $f(x)=x^2$. When squaring a value the result cannot be a negative number. So the range is:




We are talking about the interval notation. The zero is included in the interval or range.

Note: Infinity ($\infty$) must never be in the range (it always has an open limit).

A different notation would be:

$\mathbb{R}^{+}_{0}$ (set notation)

(All positive real numbers and zero included)