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. 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 open interval \((a,b)\) if for any two points \(x_1,x_2\in(a,b)\) with \(x_1

Step2: Analyze the graph

Looking at the graph, we check the behavior of the function.

• For the increasing part: There is no interval where the function is increasing.
• For the decreasing part:
• Consider the two - part of the hyperbola - like graph.
• The left - hand part of the graph (where \(x < 1\)) and the right - hand part of the graph (where \(x>1\)) are both decreasing.

Answer:

Increasing: DNE
Decreasing: \((-\infty,1)\cup(1,\infty)\)