Question

Define function?

Answer 1

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

Explanation:

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.