Question

consider the following function.
r(x)=\begin{cases}\frac{5}{8x^{5}}&\text{if }x < 1\\-\frac{3}{8}x&\text{if }x > 1end{cases}
step 1 of 3: identify the general shape and direction of the graph of this function on the interval ((-infty,1))

Explanation:

Step1: Analyze the function for $x < 1$

The function for $x<1$ is $r(x)=\frac{5}{8x^{5}}$. This is a rational - function of the form $y = \frac{k}{x^{n}}$ where $k=\frac{5}{8}$ and $n = 5$.

Step2: Determine the shape and direction

For a rational function $y=\frac{k}{x^{n}}$ with $k>0$ and $n$ odd (here $n = 5$), when $x<0$, as $x$ increases (moves from $-\infty$ to $0$), $y$ decreases (moves from $0$ to $-\infty$). When $0

Answer:

The graph is a hyper - bolic shape and is decreasing on the interval $(-\infty,1)$.