Question

the function f is graphed below. determine the intervals on which f is increasing and decreasing.

Explanation:

Step1: Recall increasing - decreasing function rules

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 left - to - right, the function is increasing when the graph goes up. We can see that the function \(y = f(x)\) is increasing on the interval \([- 3,2]\) because as \(x\) increases from \(-3\) to \(2\), the \(y\) - values of the function are getting larger.

Step3: Continue analyzing the graph

The function is decreasing on the interval \([2,5]\) since as \(x\) increases from \(2\) to \(5\), the \(y\) - values of the function are getting smaller. And it is increasing again on the interval \([5,9]\) as \(x\) increases from \(5\) to \(9\), the \(y\) - values of the function are getting larger.

Answer:

The function \(f(x)\) is increasing on the intervals \([-3,2]\) and \([5,9]\), and decreasing on the interval \([2,5]\).