Definition
Range of a function
The range of a function is the set of output values the function produces.
What it means
Think input → rule → output. Try every allowed input and collect the outputs. Repeated outputs are listed only once because a range is a set. The allowed inputs form the domain; the collected outputs form the range.
Remember it
Range is the output tray: every result the function sends out belongs there.
Example
Let f(x) = x² and let the domain be {−2, −1, 0, 1, 2}. The outputs are 4, 1, 0, 1, 4, so the range is {0, 1, 4}.
Watch for
In data work, range often means largest value minus smallest value. A function’s range is instead a set of outputs.
Common mix-up
Do not list a repeated output more than once when writing the range as a set.
Exact meaning
For a function with a stated domain, its range is the set of values f(x) obtained as x takes every allowed input in that domain.