What would the graph of $f(x) = (-e)^x$ look like? If a graph is not possible, why not?
Trying to visualise this function seems difficult as a small change in x can change the sign of f(x) but I am not sure what the formal reason as to why this function cannot be graphed. Thanks in advanced.
You can rewrite $(-e)^x$ as $(-1)^xe^x$. The real problem is with $(-1)^x$. In some sense, the "right way" to interpret that is by writing $-1=e^{\pi i}$, so its values all lie around the unit circle in the complex plane.
Multiplying a rotating term $(-1)^x$, by a growth term $e^x$, we obtain a spiral in the complex plane. It only intersects the real line when $x$ is an integer, so if you're trying to graph it in the way that we usually graph real functions, you'll end up with points at integer $x$ values, and a graph that you can't see everywhere else.
Once you study complex variables, it's not too hard to make sense of, but there are considerations that we don't have to deal with when we look at exponential functions with positive real bases.