Define function?

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Answer 1 · 2017-09-10T06:49:05

A function is a set of ordered pairs $(x,y)$ formed from a defining equation, where, for each $x$ -value there is only ONE $y$ -value

There are four relations in maths: where an $x$ -value is linked to a $y$ -value

You can have:

one $x rarr$ one $y$ value. This is a function
one $x rarr$ many $y$ values. This is not a function.

many $x$ values $rarr$ one $y$ -value. This is a function
many $x$ values $rarr$ many $y$ -values. This is not a function.

If you use an $x$ -value and you find there is a choice for the $y$ -value, that is not a function.

$y = f(x) = 3x +5$
If $x=7, rArr y = 3xx7+5 = 26 rArr (7,26)$ A function

$y = sqrt x$
$x = 25 rArr y = +5 or -5 rArr (25, +-5)$ Not a function.