# Is (-3,-2), (-1,0), (0,1), (1,2) a function?

Jul 4, 2015

Yes it is a function, i was wrong !

#### Explanation:

Jim says the correct explanation.

Two examples of functions using your points.
The particularity of your four points is their collinearity (=they are aligned).
Indeed, we can draw a straight line who is passing by all your points :

But this function is not unique, take a look of this :

Then {(-3,-2), (-1,0), (0,1), (1,2)} is a function, but you can't know more about other points. (Ex : x=2)

Jul 4, 2015

Yes, it is a function.

#### Explanation:

A function is a relation (a set of ordered pairs) with the additional property that: no two pairs have the same first element and different second elements.

The definition is often stated as: A relation in which every $x$ value is associated with exactly one $y$ value. "Exactly one means one but two or more:

So the Relation (the set) $\left\{\begin{matrix}- 3 & - 2 \\ - 1 & 0 \\ 0 & 1 \\ 1 & 2\end{matrix}\right\}$ is a function.

More examples

$\left\{\begin{matrix}- 3 & 1 \\ - 1 & 1 \\ 0 & 1 \\ 1 & 0\end{matrix}\right\}$ Is a function (no two pairs have the same $x$ and different $y$'s)

$\left\{\begin{matrix}- 2 & 0 \\ - 2 & 1 \\ 0 & 4 \\ 1 & 3\end{matrix}\right\}$ is NOT a function because the pairs $\left(- 2 , 0\right)$ and $\left(- 2 , 1\right)$ have the same first, but different second elements.