Domain Range and Function Graphic

I have been trying all day and I haven't been able to figure this homework problem out. Math is my weakest area. Can someone help me figure it out and maybe tell me how to do it? I would really appreciate it

1. Sketch a graph of the function: f(x) = 3x-2/√x^3+8

x cubed plus 8 is all under the radical

Find the function's domain and range

I really have big problems with finding domain and range. Will someone tell me what the domain and range is and how they got their answer?? Also, someone told me to use a graphic calculator to graph this but he told us not to and I don't know how to do it anyway. AHH. Help. Homework is due tomorrow and this is the only problem I have left. I really need a good grade or my school won't let me continue this program.