An operations VP has developed an efficiency$-$rating system for the various departments of her organization. The efficiency$-$rating is modeled by the following polynomial function.

$E(x)=0\mathrm{.}5x^3-3x^2+5x,$ where

$x$ is the number of new employees hired in a department, and $E(x)$ is the efficiency rating based upon the model.

A$)$ Based upon the following graph of $E(x)=0\mathrm{.}5x^3-3x^2+5x,$ what is the right$-$end behavior and the left$-$end behavior for this polynomial function written with infinity notation?

right$-$end behavio

left$-$end behavior:

shown work