Question

consider the following function.

$h(x)=\frac{10}{7}x^{5}$

step 1 of 2: identify the general shape of the graph of this function.

Explanation:

Step1: Recall power - function form

The function $h(x)=\frac{10}{7}x^{5}$ is a power function of the form $y = ax^{n}$, where $a=\frac{10}{7}$ and $n = 5$.

Step2: Analyze the exponent

Since the exponent $n = 5$ (an odd positive integer), for odd - powered power functions $y=ax^{n}$ with $a>0$, as $x\to-\infty$, $y\to-\infty$ and as $x\to+\infty$, $y\to+\infty$. The graph passes through the origin $(0,0)$ and has a smooth, continuous shape.

Answer:

The graph has a shape similar to a cubic function (but steeper), passing through the origin, decreasing on the interval $(-\infty,0)$ and increasing on the interval $(0,\infty)$.