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. there is no interval on which the function is 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 graph

Looking at the graph, we can see that as \(x\) moves from \(-5\) to \(-2\), the \(y -\)values of the function are increasing. Also, as \(x\) moves from \(1\) to \(4\), the \(y -\)values of the function are increasing.
In interval notation, the intervals where the function is increasing are \((-5,-2)\) and \((1,4)\)

Answer:

A. The function is increasing on the interval(s) \((-5,-2),(1,4)\)