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 graph

Looking at the given graph, as \(x\) moves from \(-2\) to the right (towards positive infinity), the \(y -\) values of the function are getting larger.

Answer:

A. The function is increasing on the interval\((- 2,\infty)\)