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