Question

the red dotted line shows that the function approaches ( x = 3 ).
use the graph of the function to estimate the interval on which the function is decreasing and increasing.
decreasing:
increasing:

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, as \(x\) moves from \(-1\) to \(\infty\), the \(y -\) values of the function are getting larger (the function is rising). So the function is increasing on the interval \((-1,\infty)\). As \(x\) moves from \(-\infty\) to \(-1\), the \(y -\) values of the function are getting smaller (the function is falling). So the function is decreasing on the interval \((-\infty,-1)\).

Answer:

Increasing: \((-1,\infty)\); Decreasing: \((-\infty,-1)\)