Can somebody explain to me what my graph should look like f(x)=^5√(x-4)+2

It's a curve that starts at the point (4,2), rises almost vertically for about 1 unit, then goes off right to infinity, continuously increasing but with continuously decreasing slope.

Put (x-4)^(1/5)+2 into WolframAlpha: http://www.wolframalpha.com/input/?i=%28…

For x<4, the function is complex. It's only real for x >= 4.