Answer
The graph of the given polynomial function $ f\left( x \right)=-{{x}^{4}}+8{{x}^{3}}+4{{x}^{2}}+2$ is given below.
Work Step by Step
We know that according to the Leading Coefficient Test, the end behavior of the graph of a polynomial function, $ g\left( x \right)={{a}_{n}}{{x}^{n}}+{{a}_{n-1}}{{x}^{n-1}}+\cdots +{{a}_{2}}{{x}^{2}}+{{a}_{1}}x+{{a}_{0}}$ depends on the leading coefficient $\left( {{a}_{n}} \right)$ and the degree of the polynomial.
We use the rules given on page 337 to graph the polynomial. Here, the polynomial function will have degree 4 (even) and its leading coefficient is negative so the graph will fall at both ends.
