Short Answer: True
What an illuminating question! There is a chance that you could get this wrong. I think that many people might.
Don't forget that the range is the f(x) value or the y value if it makes more sense. The y value never hits zero unless you count the value at x = - infinity. It certainly never takes on a negative value under any circumstances.
So the statement is true <<<< answer
Footnote
The domain (the x value) can go from - infinity to plus infinity. More formally
-∞ ≤ x ≤ ∞ x included in all the reals.
I've included a graph to illustrate what I've written.