Question

identify the intervals where the graph is increasing and decreasing.
increasing on the interval(s)
decreasing on the interval(s)
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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, from \(x =-\infty\) (the left - hand side) to \(x = 2\), as \(x\) increases, \(y\) decreases. From \(x = 2\) to \(x=\infty\) (the right - hand side), as \(x\) increases, \(y\) increases.

Answer:

Increasing on the interval(s): \((2,\infty)\)
Decreasing on the interval(s): \((-\infty,2)\)