What is the end behavior from a graph?

The video tutorial introduces the concept of end behavior in graph analysis, explaining how to determine what a graph does as it extends to the right or left. It covers the idea of zooming in to find extrema and zooming out to understand overall behavior. The tutorial describes how graphs can rise, fall, or approach a specific value, such as a horizontal asymptote. The explanation includes examples of graph movements and how to describe them accurately.

What descriptive terms can be used to describe the behavior of a graph that is falling?

In what scenarios would you say a graph is 'approaching' a number rather than 'rising' or 'falling'?