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

An increasing function has \(y\) - values that rise as \(x\) - values increase. A decreasing function has \(y\) - values that fall as \(x\) - values increase.

Step2: Analyze the graph

Looking at the graph, we see that for \(x> - 1\), as \(x\) increases, \(y\) decreases. For \(x < - 1\), as \(x\) increases (moving from left to right on the \(x\) - axis), \(y\) increases.

Answer:

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