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A function [math]f\,[/math] is a set or ordered pairs [math](x,y)\,[/math] no two of which have the same first member.

  • If [math]f\,[/math] is a function, the set of all elements [math]x\,[/math] that occur as first members of pairs [math](x,y)\,[/math] in [math]f\,[/math] is called the domain off. The set of second members is called the range off, or the set of values off. Therefore, for every [math]x\,[/math] in the domain off there is exactly one [math]y\,[/math] such that [math](x,y)\in f\,[/math]

  • Since [math]y\,[/math] is uniquely determined once [math]x\,[/math] is known, we can introduce a special symbol for it. It is customary to write


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

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