Answer
$f(x)=(-x+6)^3-6$
Work Step by Step
Since the shape of the graph is a $f(x) = x^3$ we will start with that function:
$f(x)=x^3$
The first transformation is 6 units left. Remember that shifts to the left or right are done inside of the function and that left or right transformations have an opposite sign so that left shifts are positive and right shifts are negative.
$f(x)=(x+6)^3$
The second transformation is six units down. Up and down transformations are added to the right side. Up is positive and down is negative.
$f(x)=(x+6)^3-6$
The reflection is across the y-axis. Y-axis reflections mean changing the sign of the x on right side.
$f(x)=(-x+6)^3-6$
