Question

consider the following function. h(x) = \frac{3}{5x^{3}} step 1 of 2 : identify the general shape of the graph of this function.

Explanation:

Step1: Analyze the function type

The function $h(x)=\frac{3}{5x^{3}}$ is a rational - function of the form $y = \frac{k}{x^{n}}$ where $k=\frac{3}{5}$ and $n = 3$.

Step2: Recall the properties of $y=\frac{k}{x^{n}}$

For odd - powered rational functions of the form $y=\frac{k}{x^{n}}$ ($n$ odd), the graph has two branches. When $k>0$, as $x\to+\infty$, $y\to0^{+}$ and as $x\to-\infty$, $y\to0^{-}$. The graph is in opposite quadrants (quadrants I and III).

Answer:

The graph has two branches in opposite quadrants (quadrants I and III), approaching the $x$ - axis and $y$ - axis as asymptotes.