Graphing an exponential function

Hello, I need to graph g(x)= -2^x using x values -2,-1,0,1,2 and find all asymptotes. I was under the impression that an exponential function with base b is defined as follows: f(x)=b^x Where b is greater than 0, b cannot =1, and x is any real #......if this is true, -2 is NOT greater than 0, hence my confusion. I plotted the given points but they don't seem to form a normal looking exponential function graph. I also can't seem to figure out where the asymptotes fall from the points I've plotted. Any insight on this would be most helpful, Thanks ~CC

I think you're graphing instead of . There is a big difference.

For example, if we take x = 2, we have:
but

For the former graph, you will get a bunch of scattered points that don't form a smooth curve. However, the latter graph produces but reflected over the x-axis.