Respuesta :
We will investigate the property of a function.
A function is defined as " Each input of a function there must only be a unique output ".
On a graph this can be defined by a vertical line test. All functions must qualify the vertical line test! The test is basically scoring vertical lines on a gragh plot of a relationhsip. No vertical line must cross or meet or cut the graph at more than one point for the relationhsip to be classified as a "function".
The input values ( domain ) and output value for each are expressed below:
[tex]\begin{gathered} \text{ }\text{\textcolor{#FF7968}{Domain : }}\left\lbrace \text{ - 1 , 2 , 3 , 6 }\right\rbrace \\ \text{\textcolor{#FF7968}{Range:}}\text{ }\left\lbrace \text{ -2 , -1 , 2 , 3 , 4 }\right\rbrace \end{gathered}[/tex]The total number of domain values are ( 4 ), where the total number of range values are ( 5 ).
The above statement implies that for any one of the domain value has two values of output value.
The above statement is a direct negation of the definition of what constitute a function f ( x ) i.e:
[tex]\text{Each input value ( domain ) must have a unique output value ( range ).}[/tex]Therefore, the given expression is:
[tex]\textcolor{#FF7968}{The}\text{\textcolor{#FF7968}{ relation is NOT a function!}}[/tex]