Question

identify the intervals where the graph is increasing and decreasing. if there is more than one interval, use a union u to combine them.

Explanation:

Step1: Recall the definition of increasing and decreasing

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

• Look at the slope of the graph. The graph has a "valley - peak - decline" structure.
• From the left - hand side (as \(x\) approaches \(-\infty\)) up to \(x=-1\), the function is decreasing.
• From \(x = - 1\) to \(x=2\), the function is increasing (because as \(x\) increases from \(-1\) to \(2\), the \(y\) - values of the function increase).
• From \(x = 2\) to the right - hand side (as \(x\) approaches \(\infty\)), the function is decreasing.

Answer:

The function is increasing on the interval \((-1,2)\) and decreasing on the intervals \((-\infty,-1)\cup(2,\infty)\)