Question

question 4
from the graph of a function above, find the interval(s) of x - values where the function is
(a) increasing :
(b) decreasing :

Explanation:

Step1: Recall the definition of increasing and decreasing functions

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 graph

Looking at the graph:

• For the increasing intervals:
• From \(x=-3\) to \(x = - 2\), as \(x\) increases, \(y\) increases.
• From \(x = 1\) to \(x=\infty\) (in the context of the graph's visible right - hand behavior), as \(x\) increases, \(y\) increases.
• For the decreasing intervals:
• From \(x=-\infty\) (in the context of the graph's visible left - hand behavior) to \(x=-3\), as \(x\) increases, \(y\) decreases.
• From \(x=-2\) to \(x = 1\), as \(x\) increases, \(y\) decreases.

Answer:

(a) The function is increasing on the intervals \((-3,-2)\cup(1,\infty)\)
(b) The function is decreasing on the intervals \((-\infty,-3)\cup(-2,1)\)