Answer
The graph of the given polynomial function $ f\left( x \right)=-2{{x}^{3}}+6{{x}^{2}}+3x-1$ is given below:
Work Step by Step
We now 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 graph has an odd degree and negative leading coefficient, so it rises to the left and falls to the right.
