# Function

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Definition
 Function A function $f\,$ is a set or ordered pairs $(x,y)\,$ no two of which have the same first member. If $f\,$ is a function, the set of all elements $x\,$ that occur as first members of pairs $(x,y)\,$ in $f\,$ is called the domain off. The set of second members is called the range off, or the set of values off. Therefore, for every $x\,$ in the domain off there is exactly one $y\,$ such that $(x,y)\in f\,$ Since $y\,$ is uniquely determined once $x\,$ is known, we can introduce a special symbol for it. It is customary to write $y=f(x)\,$

## Examples

A function can be though as a table consisting of two columns. Each entry in the table is an ordered pair $(x,f(x))\,$ ; the column of $x\,$'s is the domain off, and the column of $f(x)\,$ 's, the range.

$\text{Polynomial Function }\,$$f(n)=3n^2+n-5\,$
$n\,$ $f(n)\,$
$-5\,$ $65\,$
$-4\,$ $39\,$
$-3\,$ $19\,$
$-2\,$ $5\,$
$-1\,$ $-3\,$
$0\,$ $-5\,$
$1\,$ $-1\,$
$2\,$ $9\,$
$3\,$ $25\,$
$4\,$ $47\,$
$5\,$ $75\,$