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 interval if, for any two points \(x_1\) and \(x_2\) in the interval with \(x_1

Step2: Analyze the given graph

Looking at the graph, we can see that the function rises (is increasing) from \(x = 1\) to \(x = 2\) and from \(x = 4\) to \(x = 5\). In interval notation, these intervals are \((1,2)\) and \((4,5)\)

Answer:

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