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 2 of 3: identify the general shape and direction of the graph of this function on the interval ((1,infty)).

Explanation:

Step1: Analyze the function for \(x>1\)

For \(x > 1\), \(r(x)=-\frac{3}{8}x\). This is a linear - function of the form \(y = mx + b\) where \(m=-\frac{3}{8}\) and \(b = 0\).

Step2: Determine the shape and direction

Since the slope \(m=-\frac{3}{8}<0\), the graph is a straight - line. As \(x\) increases, \(y\) decreases.

Answer:

The graph is a straight - line that slopes downwards as \(x\) increases on the interval \((1,\infty)\).