Answer
See below.
Work Step by Step
1st step (black graph): The parent function: $y=x^3$
2nd step (green graph): Stretch by a factor of 3: $y=3x^3$
3rd step (red graph): Shift 2 units down: $y=3x^3-2$
Final step (blue graph): Shift left 1 unit. $y=3(x+1)^3-2$
