00:01
So in this question, they say assume that y equals fx is a function that is continuous on the real line.
00:10
We want to know which of the following statements must be true about the graph of f of x.
00:17
And it turns out this time that a is going to be my answer.
00:23
The graph of y equals f of x can have either no horizontal asymptote, one horizontal asymptote, or two distinct horizontal asymptotes.
00:35
Let me show you examples of each of these.
00:39
So, for example, if you had something like y equals x, okay, y equals x is something that looks like this.
00:51
This graph has no horizontal asymptotes.
00:57
So that's one possibility.
01:03
Another possibility is suppose i had something like y equals 1 over x squared plus 1.
01:14
Y equals 1 over x squared plus 1.
01:17
You may have seen this before.
01:18
It is a bell shaped graph.
01:22
It is a bell shaped graph that looks like this...