Question

consider the following function. (h(x)=-\frac{5}{8}x^{5}). step 1 of 2: identify the general shape of the graph of this function.

Explanation:

Step1: Analyze the degree and leading - coefficient

The function $h(x)=-\frac{5}{8}x^{5}$ is a polynomial function. The degree $n = 5$ (an odd number) and the leading - coefficient $a=-\frac{5}{8}<0$.

Step2: Determine the end - behavior

For a polynomial function $y = ax^{n}$ with $n$ odd and $a<0$, as $x\to+\infty$, $y\to-\infty$ and as $x\to-\infty$, $y\to+\infty$. The general shape of the graph of an odd - degree polynomial is similar to that of a cubic function but with more "bend". It starts from the upper left quadrant and ends in the lower right quadrant.

Answer:

The graph starts in the second quadrant and ends in the fourth quadrant.