Question

determine the open intervals where the function graphed below is increasing and where the function is decreasing. enter \dne\ if an interval does not exist. round to the nearest 0.5 as necessary. increasing: decreasing: question help: video post to forum

Explanation:

Step1: Recall the definition of increasing and decreasing functions

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:

• The function is increasing on the intervals \((-1.5,6)\) (because as \(x\) moves from \(-1.5\) to \(6\), the \(y\) - values of the function are getting larger).
• The function is decreasing on the intervals \((-7,-1.5)\) and \((6,7)\) (because as \(x\) moves from \(-7\) to \(-1.5\) and from \(6\) to \(7\), the \(y\) - values of the function are getting smaller).

Answer:

Increasing: \((-1.5,6)\)
Decreasing: \((-7,-1.5)\cup(6,7)\)