Answer
1st step (black graph): The parent function: $y=x^3$
2nd step (green graph): Flipped over the x-axis. $y=-x^3$
3rd step (red graph): Stretched by a factor of 2. $y=-2x^3$
4th step (orange graph): Shifted 8 units down. $y=-2x^3-8$
Final step (blue graph): Shifted 2 units to the left. $y=-2(x+2)^3-8$
The x-intercept is $(-\sqrt[3]4-2,0)$
The y-intercept is (0,-24)
The domain is $(-\infty,\infty)$
The range is $(-\infty,\infty)$
Work Step by Step
The x-intercepts are all points of a graph when f(x)=0 while the y-intercepts are all points of a graph when x=0.
The domain is a horizontal span from the function's smallest value of x to the function's largest value of x.
The range is a vertical span from the function's smallest value of f(x) to the function's largest value of f(x).