Question

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

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

Looking at the graph:

• From \(x=-4\) to \(x = - 2\), the function is decreasing (it goes down as we move from left - to - right).
• From \(x=-2\) to \(x = 1\), the function is increasing (it goes up as we move from left - to - right).
• From \(x = 1\) to \(x=2\), the function is decreasing.
• From \(x = 2\) to \(x=4\), the function is increasing.

Answer:

\((-2,1),(2,4)\)