For the fixed design nonparametric regression, boundary effects on kernel estimators are of two types. One is caused by the fact that the number of observations applied to kernel estimators in boundary regions is smaller than that in the interior. The other is caused by the jump points of the regression function or its derivatives. To deal with boundary effects of these two types, an extrapolation method is proposed to reuse the observations on boundary regions and neighborhoods of the jump points. The resulting regression function estimate is of the same performance as that obtained by a kernel estimator with boundary modification in the case that the regression function has continuous derivatives, in the sense of the mean average square error. If the derivatives of the regression function have jump points, then the resulting regression function estimate shows continuities at these jump points. For applications, a bandwidth selector is proposed. Almost sure convergence and asymptotic normality for the bandwidth produced by this bandwidth selector are proved.