We are given the different values for x and y in the table to be
[tex]\begin{gathered} (2,0) \\ (2,-2) \\ (2,3) \end{gathered}[/tex]
To get the option that best defines the table
We can get the equation of a line that conforms to the given points
[tex]\frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}[/tex]
So we can use the first two points
[tex](2,0)\text{ and (2,-2)}[/tex]
[tex]\begin{gathered} \frac{y-0}{x-2}=\frac{-2-0}{2-2} \\ \\ \frac{y}{x-2}=-\frac{2}{0} \end{gathered}[/tex]
If we cross multiply
[tex]\begin{gathered} y\times0=2(x-2) \\ 0=2x-4 \\ 2x=4 \\ x=\frac{4}{2} \\ x=2 \end{gathered}[/tex]
Thus the equation of the line is
[tex]x=2[/tex]
The graph of the function is given as
[tex]x=2[/tex]
The graph of the function is
The best option that best defines the function is option D
