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 given graph

Looking at the graph of \(y = f(x)\):

• For the interval \([-4,-1]\), as \(x\) increases from \(-4\) to \(-1\), the \(y\) - values of the function decrease.
• For the interval \([0,4]\), as \(x\) increases from \(0\) to \(4\), the \(y\) - values of the function decrease.

Answer:

The function \(f(x)\) is decreasing on the intervals \([-4,-1]\) and \([0,4]\).