select the correct answer from each drop - down menu.\nthe table shows certain values of a cubic…

Explanation:

Step1: Identify relative maximum

A relative maximum is a point where the function changes from increasing to decreasing. Looking at the $y$-values in the table, as $x$ moves from -7 to - 4, $y$ values decrease from 216 to 0. As $x$ moves from -4 to 0, $y$ values first increase (from 0 to 20). As $x$ moves from 0 to 3, $y$ values increase further from 20 to 56. Then as $x$ moves from 3 to 7, $y$ values decrease from 56 to - 176. The $y$-value of 56 at $x = 3$ is a local high - point compared to its neighboring points. So the function has a relative maximum when $x$ is near 3.

Step2: Analyze end - behavior for positive infinity

For a cubic function of the form $y=ax^{3}+bx^{2}+cx + d$, if the leading coefficient $a<0$, as $x\rightarrow+\infty$, $y\rightarrow-\infty$. By observing the trend of the $y$-values as $x$ increases from 3 to 7 (where $y$ goes from 56 to -176), we can see that as $x$ approaches positive infinity, the value of the function approaches negative infinity.

Answer:

The function has a relative maximum when $x$ is near 3. As $x$ approaches positive infinity, the value of the function approaches negative infinity.