Question

determine all intervals on which the graph of ( f ) is decreasing.

Explanation:

Step1: Recall the definition of a decreasing function

A function \(y = f(x)\) is decreasing 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 of \(y = f(x)\), we observe the following:

• For \(x\in(-\infty,- 6)\), as \(x\) increases (moves from left - to - right), the \(y\) - values of the function decrease.
• For \(x\in(0,4)\), as \(x\) increases (moves from left - to - right), the \(y\) - values of the function decrease.

Answer:

\((-\infty,-6)\) and \((0,4)\)