I understand how to create a horizontal phase line of a function...

--->-----(-5)-----<------(0)------<------(3)----->----

...but I don't really understand what it means. What does the horizontal line represent and what do the arrows represent?

And what procedure would I use for answering the question:

The solution of the above equation with is defined on the interval , find

Is there a way to find the limit analytically? I'm guessing not since we're using the phase line to do it.