Answer
The graphs of the given polynomial functions $ f\left( x \right)=-{{x}^{4}}+2{{x}^{3}}-6x $ and $ g\left( x \right)=-{{x}^{4}}$ are shown 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, both functions have degree 4 (even), and both of their leading coefficients is negative so, the graphs fall to the left and right.
