Graph the function \( f(x) = x^{3} - 6x^{2} + 9x + 15 \) and determine its x-intercepts.

Step 1 ：Step 1: For graphing the function \( f(x) = x^{3} - 6x^{2} + 9x + 15 \), we need to plot a number of points and then connect them to get the general shape of the curve. To do this, we can choose a range of x-values and then compute the corresponding y-values.

Step 2 ：Step 2: To find the x-intercepts, we need to solve the equation \( f(x) = 0 \). Therefore, we solve \( x^{3} - 6x^{2} + 9x + 15 = 0 \).