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Let’s say we have 100 people and we give every single one single one of them a dart(as in [darts the sport](https://nl.m.wikipedia.org/wiki/Darts_(sport))). We draw one small point on the wall and put the candidates a big distance away, the and one with the dart closest to the middle will win a prize we give away. What would we expect from the distance and place of the darts?

Well, we’d expect for the distance that there’d be a few lucky ones really close to the middle and a few really far away, but most would be about the same distance. But not around the same place probably.

Here’s drawings of what it would probably look like [http://imgur.com/a/QfNqSDD](http://imgur.com/a/QfNqSDD). What if we wanted to make a function for the distance of the darts?

First a definition. There’s two types to connect variables:

– function: one input gives one output, but one output can have multiple inputs.

Example: the function y = f(x) = x²

One x only has one y, for example 2² = 4 and only 4

One y can have multiple x’s, for example f(x) = 4, then x can be 2 or -2

– curve: this does have multiple inputs.

Example: the inverse of sin(x)

If you look at the graph of y=sin(x) you’ll see that if you take the inverse(that is, write in form x=… and replace x for y and y for x) you wouldn’t have a function anymore.

##So how to use it?

Let’s say you name the horizontal plane x in cm and vertical y in cm. The point you drew is (0,0). So if you go 1cm to the right you end up in (1,0). One up from the origin point in (0,1). For both the distance is just 1 cm. If the point is on (3,4), then you can’t just look at one distance, but you can just Pythagoras: Distance = √3²+4² = √25 = 5.

Now what if the points are around a distance of 20cm from the point you drew? That means now you can estimate for all points that:

√x² + y² = 25

Ofcourse this can be written as function of y or x, but you can’t if:

√x²+y²+z² = 25

There’s also multivariable functions. The difference between multivariable functions and a curve is that a curve isn’t a function, basically an equation. a multivariable function does have a function with an output looking like this: f(x,y,…) = …

##Then when do you use these and not just a function?

Like I just said, with two dimensions it isn’t really needed to write something as a curve. However if you go with more variables, it might sometimes be too complicated to write something as a function of one variable and write it as a curve with those two sides that are equal instead.