Answer:
D: It is not a function because there are two different [tex]y[/tex]-values for a single [tex]x[/tex]-value.
Step-by-step explanation:
Definition: A function is a rule which relates the values of one variable quantity [tex](x)[/tex] to the values of another variable quantity [tex](y)[/tex], and does so in such a way that the value of [tex]y[/tex] is uniquely determined by the value of [tex]x[/tex].
This means that for one value of variable [tex]x,[/tex] there must be an unique value of [tex]y.[/tex]
The diagram shows two points [tex](4,-2)[/tex] and [tex](4,4)[/tex]. Hence,
[tex]-2=f(4)\\ \\4=f(4)[/tex]
Since for one value of [tex]x=4,[/tex] there are two different values of [tex]y: \ y=-2[/tex] and [tex]y=4[/tex], you can state that the graph does not represent the function.
Correct option is D: It is not a function because there are two different [tex]y[/tex]-values for a single [tex]x[/tex]-value.
