I can plot points on the coordinate plane only when my x value is integer. What's happening on the graph when x is fraction? My calculator breaks raising a negative number to a fractional exponent.
This website can't graph the function either: https://www.desmos.com/calculator/xucwdp4dz3
Can we graph that function somehow?
That function is not defined in a lot of points on the real axis. For example, if you take $x=\frac{1}{2}$ then $(-2)^x=(-1)^x*2^x=\sqrt{-1}*\sqrt{2}$, so you are taking a square root of a negative number here and hence the function is not defined at $x=\frac{1}{2}$. So to do something with this function you need to work in the complex plane, and even then there will be some problems.