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 \((a,b)\) if for any two points \(x_1\) and \(x_2\) in \((a,b)\) with \(x_1

Step2: Analyze the left - hand side of the graph

Looking at the left - hand side of the graph (the part to the left of the local minimum in the second quadrant):
As \(x\) moves from \(-\infty\) to \(-4\), the \(y\) - values of the function are decreasing.

Step3: Analyze the right - hand side of the graph

Looking at the right - hand side of the graph (the part to the left of the local minimum in the fourth quadrant):
As \(x\) moves from \(0\) to \(4\), the \(y\) - values of the function are decreasing.

Answer:

The function \(f(x)\) is decreasing on the intervals \((-\infty,-4)\) and \((0,4)\)