Question

determine all intervals on which the graph of $f$ is increasing.

Explanation:

Step1: Recall the definition of an increasing function

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 left - hand part of the graph:
• From \(x =-\infty\) to \(x=-4\), as \(x\) increases, \(y = f(x)\) increases.
• Look at the right - hand part of the graph:
• From \(x = 6\) to \(x=\infty\), as \(x\) increases, \(y = f(x)\) increases.

Answer:

The function \(f(x)\) is increasing on the intervals \((-\infty,-4)\) and \((6,\infty)\)