Range
Given its domain, the range of a function is the set of all values to which a function is defined.
!
Remember
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
Example
Following function is given $f(x)=x^2$. When squaring a value the result cannot be a negative number. So the range is:
$[0,\infty[$
i
Hint
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).
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)