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. the function is increasing on the interval(s) $(-\infty, 2),(3,4)$.
(type your answer in interval notation. use a comma to separate answers as needed.)
b. the function is never increasing.

(b) select the correct choice below and, if necessary, fill in the answer box to complete your choice.
oa. the function is decreasing on the interval(s)
(type your answer in interval notation. use a comma to separate answers as needed)
ob: the function is never decreasing

Explanation:

Step1: Analyze the function's behavior

A function \(y = f(x)\) is increasing when, as \(x\) increases, \(y\) also increases. It is decreasing when, as \(x\) increases, \(y\) decreases.

Step2: Identify the decreasing intervals

Looking at the graph, from \(x = 2\) to \(x = 3\) and from \(x=4\) to \(+\infty\), as \(x\) increases, the \(y -\)values of the function decrease.

Answer:

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