Solution
For this case we have the following conditions:
Vertical reflection across the x axis
Horizontal compression of 1/3
Vertical shift down 4 units
The parent function is y= x³
A vertical reflection implies: y= - x³
The horizontal compression of 1/3 implies: y= - (3x)³
And the vertical shift down 4 units implies: y= -(3x)³ -4
Then the correct answer is the first one:
y= -(3x)³ -4