Consider the following set of data points in the table below:

$(4\mathrm{.}1)$ Using guidepoints of your choice from the data set, construct the connected Bezier curve from the set of points. $($Hint: Divide the set of points into three parts$)$

$(4\mathrm{.}2)$ Draw the connected Bezier polynomial $.$

$(4\mathrm{.}3)$ Why is the graph smoothly connected at points $3$ and $6?$