As x-> 1+, f(x) -> -infinity, e^[f(x)] -> 0+
As x-> +infinity, f(x) -> 0-, e^[f(x)] -> 1-
As x-> 1-, f(x) -> +infinity, e^[f(x)] -> +infinity
At f(x) = 2, e^[f(x)] = e^2
etc.
Basically break it up and use what you know about exponentials to get the general shape of the graph and sketch.