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 \(f(x_1)<f(x_2)\). Visually, the graph of the function rises as we move from left - to - right on the interval.

Step2: Analyze the given graph

Looking at the graph, we can see that the function rises (is increasing) on the intervals \((-6,-5)\) and \((-2,-1)\).

Answer:

A. The function is increasing on the interval(s) \((-6,-5),(-2,-1)\)