# how come for any given f(x) a y could have multiple values of x, while x has only a single y value [duplicate]

I guess i might be answering my own question here, but is it because of how we chose to represent our functions? That is, for the lack of better term, strech it along the x axis? Has it it been f(y) would it be the other way around?

A function from some set $X$ to $\mathbb R$ is, by definition, a specific type of relation, which is a collection of pairs, $f\subseteq \{(x, y)\in X\times \mathbb R\}$. $f$ is a function if each $x\in X$ appears in precisely one pair in $f$, which is why you can write $f(x) = y$ instead of $(x,y)\in f$.
The definition of a mapping states that each anticident in the initial set i.e each $x$ shall have one and only one image in the final set moreover this mapping can be a non injective mapping thus there exist maybe more than 1 $image$ $y$ having more than one anticident $x$ ! Note that the anticidents are different as stated in the beggining so you can call the relation $f$ a mapping. Thats why every $x$ in a mapping is related to only 1 image while there may exist Images that are related to several different Anticidents.