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According to study about convex function, A. W. Roberts and D. E. Varberg[17] have studied further. In this paper, we will introduce some basic properties about convex function and quasiconvex fucnction on R. Some comparison between properties of convex function and quasiconvex function will be presented also. Our results are quasiconvex function can be represented as monotone function either or at most as two combination of monotone functions, as consequences it is discontinuous mostly at countable points, and it is not differentiable at zero measure set only. However the results are still fundamental, but we will learn as clear as we can.