if you have a relation with the domains: 0,1,2,3,4 and a range of: 3,1,2,4,2 does this mean it is not a function because there are two outputs of the number 2? Or can it only not be function if there are two of the same inputs with a different output?
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1$\begingroup$ The second one. $\endgroup$– BerciSep 2, 2015 at 23:41
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$\begingroup$ It's not a function if for some value $x$ you'd have different values of $y$. Let's say you have a random function $f(x)$ and you plug in $x=1$, if it would show something like $f(1) = 2$ and $f(1)= 3$, it wouldn't be a function. The reverse is true though, wherein if you have $f(1)=2$ and $f(2)=2$, it would still be a function. $\endgroup$– mopySep 2, 2015 at 23:48
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A function can be described as a cartesian product of the domain and the range, so the relation you describe is a function. You are correct when saying that a function can't have an input with two different outputs
