Answer
$$
f(x)=(x+1)^{3}-2
$$
The given graph is the graph of
$$
y=x^{3}
$$
translated 1 units to the left and 2 units downward.
Work Step by Step
$$
f(x)=(x+1)^{3}-2
$$
The given graph is the graph of
$$
y=x^{3}
$$
translated 1 units to the left and 2 units downward.