Let
g(x)--------> the translation of the function f(x)
we know that
the rule of the translation is
[tex]3[/tex] units left and [tex]2[/tex] units down
that means
[tex](x,y)-------> (x-3,y-2)[/tex]
so
In the function f(x) the point [tex](0,0)[/tex] is equal at the point [tex](-3,-2)[/tex] in the function g(x)
therefore
the function g(x) is equal to
[tex]g(x)=f(x+3)-2[/tex]
[tex]g(x)=(x+3)^{3} -2[/tex]
The answer is
a) the rule of the translation is [tex](x,y)-------> (x-3,y-2)[/tex]
b) The graph in the attached figure
