Answer
(a)$$g(x)=-x^3+3x^2+1$$
(b)$$g(x)=(x-2)^3+3(x-2)^2+1$$
Work Step by Step
(a)
We can get the graph of the function $g$ from the the graph of $f$ by first reflecting the graph of $f$ about the $x$-axis, so$$x^3-3x^2 \quad \longrightarrow \quad -(x^3-3x^2),$$and then shifting it vertically up one unit, so$$-(x^3-3x^2) \quad \longrightarrow \quad -(x^3-3x^2)+1=-x^3+3x^2+1 .$$
(b)
We can get the graph of the function $g$ from the graph of $f$ by first shifting the graph of $f$ horizontally to the right two units, so$$x^3-3x^2 \quad \longrightarrow \quad (x-2)^3-3(x-2)^2,$$and then shifting it vertically up one unit, so$$(x-2)^3-3(x-2)^2 \quad \longrightarrow \quad (x-2)^3-3(x-2)^2+1.$$
