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, on the graph, the function rises from left - to - right.
Looking at the given graph, we can observe the part of the graph where it is rising.

Step2: Identify the interval

We can see that the function is increasing on the interval \((1,2)\)

Answer:

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