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) (1,2),(3,4)
(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

Step2: Analyze the graph

Looking at the graph, as we move from left - to - right on the interval \((1,2)\), the \(y\) - values of the function are rising. Also, as we move from left - to - right on the interval \((3,4)\), the \(y\) - values of the function are rising.

Answer:

A. The function is increasing on the interval(s) \((1,2),(3,4)\)