Question

Determine whether the relation is a function.

Input, xOutput, y01.411.62\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 XX, the domain of the function is singly associated or not with a set of yy, the range of the function.

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

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