SOLUTION: When a function has an asymptote of y=-3, what's the rage?

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Question 887510: When a function has an asymptote of y=-3, what's the rage?
Found 2 solutions by jim_thompson5910, Edwin McCravy:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Assuming the function does NOT cross over the horizontal asymptote, the range is the set of all real numbers such that y can be any number but -3



Range in Descriptive English: The output of the function is any number but -3.


Range in Set-Builder Notation:


Range in Interval Notation:

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
The other tutor only told you of one case, when the graph extends forever
upward above the asymptote y=-3 and also forever below it.

This case: (-infinite,-3)U(-3,infinity),

but that's not the only possibility.

Sometimes the range is just (-infinity,-3) when the graph is all below
the asymptote y=-3, and extends forever downward, but no part of the
graph is above the asymptote y=-3

Sometimes it's just (-3,infinity), when the graph is all above
the asymptote y=-3, and extends forever upward, and no part of the
graph is below the asymptote y=-3

And that's not all either:

Here's a graph where the range is only (-3,-1):



He mentioned the case where the graph crosses the asymptote. In that
case the range could be anything and would include -3.

So you see there are more possibilities for the range besides just that one.

Edwin