TITLE: How do you graph a negative number raised to $x$?
QUESTION [7 upvotes]: As a freshman in High School, this may be a ridiculous or simple question, but what does a graph look like of something like $y=(-1)^x$? While I imagine that the graph is more or less a dotted line across $y=1$ and $y=-1$, are there are undefined points? How do fractional exponents interact with their negative subjects?

REPLY [2 votes]: As others mention, this graph will have many points where it will not be defined. In any finite interval like $(0,1)$ there would be infinitely many points where this function is discontinuous.
Consider $f(x) = (-1)^{x}$  and $x = \frac{p}{q},$ where $p,q$ are mutually prime integers. Now if $q$ is even, $f(x)$ will not be real.