## Answer :

[tex]\[ \begin{tabular}{|c|c|c|c|c|c|c|} \hline $x$ & -5 & -4 & -3 & -2 & -1 & 0 \\ \hline $g(x)$ & -1 & 0 & -1 & -4 & -9 & -16 \\ \hline \end{tabular} \][/tex]

1. We need to determine where the minimum value of the function [tex]\( g(x) \)[/tex] occurs. The minimum value is the smallest value of [tex]\( g(x) \)[/tex] present in the table.

2. We observe the values of [tex]\( g(x) \)[/tex]:

- When [tex]\( x = -5 \)[/tex], [tex]\( g(x) = -1 \)[/tex]

- When [tex]\( x = -4 \)[/tex], [tex]\( g(x) = 0 \)[/tex]

- When [tex]\( x = -3 \)[/tex], [tex]\( g(x) = -1 \)[/tex]

- When [tex]\( x = -2 \)[/tex], [tex]\( g(x) = -4 \)[/tex]

- When [tex]\( x = -1 \)[/tex], [tex]\( g(x) = -9 \)[/tex]

- When [tex]\( x = 0 \)[/tex], [tex]\( g(x) = -16 \)[/tex]

3. From these values, we see:

- The maximum value of [tex]\( g(x) \)[/tex] is [tex]\( 0 \)[/tex] at [tex]\( x = -4 \)[/tex].

- The minimum value of [tex]\( g(x) \)[/tex] is [tex]\( -16 \)[/tex] at [tex]\( x = 0 \)[/tex].

4. Since the minimum value of the function [tex]\( g(x) \)[/tex] occurs at the point where [tex]\( x = 0 \)[/tex], this point is the y-intercept of the function.

Therefore, the correct statement is:

D. The minimum occurs at the function's y-intercept.