Question

use the graph to determine
a. open intervals on which the function is increasing, if any
b. open intervals on which the function is decreasing, if any
c. open intervals on which the function is constant, if any
a. select the correct choice below and, if necessary, fill in the answer box to complete your choice.
○ a. the function is increasing on the interval(s) (type your answer in interval notation. use a comma to separate answers as needed )
○ b. the function is never increasing

Explanation:

Step1: Recall the definition of an increasing function

A function \(y = f(x)\) is increasing on an open interval \((a,b)\) if for any \(x_1,x_2\in(a,b)\) with \(x_1 < x_2\), we have \(f(x_1)<f(x_2)\).

Step2: Analyze the given graph

Looking at the graph, as \(x\) increases, the \(y -\) values of the function are always getting smaller. There is no part of the graph where as \(x\) increases, \(y\) also increases.

Answer:

B. The function is never increasing.