Question

Determine whether the relation is a function.$\begin{matrix} \text{Input, x} & \quad & \text{Output, y}\\ & \quad & \text{0}\\ \text{1.4} & \stackrel { \nearrow } { \searrow } & \text{1}\\ \text{1.6} & \stackrel { \nearrow } { \searrow } & \text{2}\\ \end{matrix}$

Solution

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For identify whether the given relation is a function or not, we have to check that each element of a set $X$, the domain of the function is singly associated or not with a set of $y$, the range of the function.

In given relation, the $x=1.4$ and $x=1.6$ each have two values in the set of $Y$ these are, for $x=1.4$ values of $y=0,1$ and for $x=1.6$ the values of $y=1,2$ thus the set of $X$ is not singly associate with the set of $Y$. Hence the given relation is not a function

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