Question

list the interval(s) on which f is decreasing. the interval(s) on which f is decreasing is/are (type your answer in interval notation. use a comma to separate answers as needed.)

Explanation:

Step1: Recall the definition of a decreasing function

A function \(y = f(x)\) is decreasing on an interval \((a,b)\) if for any two points \(x_1\) and \(x_2\) in \((a,b)\) with \(x_1

Step2: Analyze the graph

Looking at the graph, we can observe two intervals where the function is decreasing.

• For the first part of the decreasing interval:
• We start from \(x = 1\) (approximate \(x\) - value of the local maximum) and go to \(x = 2\) (approximate \(x\) - value of the local minimum).
• In interval notation, this is \((1,2)\).
• For the second part of the decreasing interval:
• We start from \(x=- 8\) (approximate \(x\) - value of the local maximum on the left - hand side) and go to \(x=-6\) (approximate \(x\) - value of the local minimum on the left - hand side). In interval notation, this is \((-8,-6)\).

Answer:

\((-8,-6),(1,2)\)