Question

consider the following function.
q(x)=\begin{cases}\frac{1}{2x}&\text{if }x < 2\\-\frac{4}{3}x&\text{if }x>2end{cases}
step 2 of 3: identify the general shape and direction of the graph of this function on the interval ((2,infty)).

Explanation:

Step1: Analyze the function for \(x>2\)

The function for \(x > 2\) is \(q(x)=-\frac{4}{3}x\). This is a linear - function in the form \(y = mx + b\) (where \(b = 0\) and \(m=-\frac{4}{3}\)).

Step2: Determine the shape and direction

For a linear function \(y=mx + b\), when \(m<0\), the graph is a straight - line. The negative slope \(m =-\frac{4}{3}\) means the line is decreasing.

Answer:

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