Question

consider the following function.
r(x)=\begin{cases}-\frac{5}{8}x&\text{if }x < - 2\\frac{2}{3}sqrt3{x}&\text{if }xgeq - 2end{cases}
step 1 of 3: identify the general shape and direction of the graph of this function on the interval ((-infty,-2)).

Explanation:

Step1: Analyze the function on the interval

On the interval $(-\infty, - 2)$, the function is $r(x)=-\frac{5}{8}x$. This is a linear - function of the form $y = mx + b$ (where $b = 0$ and $m=-\frac{5}{8}$).

Step2: Determine the shape and direction

For a linear function $y = mx + b$, the shape of the graph is a straight - line. The slope $m =-\frac{5}{8}<0$. When the slope of a linear function is negative, the line is decreasing.

Answer:

The graph is a straight - line and is decreasing on the interval $(-\infty, - 2)$.