Suppose we fit a smoothing spline on n data points (x_i, y_i) where x_i's are unique and arranged in an increasing order. Which of the following statements are correct? Circle all that apply.

1. Due to the roughness penalty, the fitted curve is no longer a piecewise cubic polynomial function.
2.		When the tuning parameter lambda is set to be zero, the curve returned by smoothing spline passes through all the data points (x_i, y_i).
3.		When the tuning parameter lambda is set to be zero, smoothing spline is equivalent to cubic polynomial regression.
4.		The fitted curve is a piecewise cubic polynomial when x is between x_1 and x_n, but a linear function when xx_n.
5.		Instead of tuning lambda, we can tune the degree of the freedom of a smoothing spline model (i.e., the df option in smooth.spline command). But we can only try integer values for df.
6.		When the tuning parameter lambda is equal to infinity (or large enough), smoothing spline is equivalent to linear regression.
7.		When the tuning parameter lambda is equal to infinity (or large enough), smoothing spline is equivalent to cubic polynomial regression.
8.		The data points divide the x-coordinate into (n+1) intervals, and the fitted curve is a linear function within each interval.