Notice that the graph of f(x) includes the point (0,0); therefore, apply each one of the listed transformations to (0,0) as shown below
[tex]\begin{gathered} (0,0)\rightarrow(2,0) \\ (0,0)\rightarrow(-0,0)=(0,0) \\ (0,0)\rightarrow(0,-2) \\ (0,0)\rightarrow(0,2*0)=(0,0) \end{gathered}[/tex]
Thus, the only possibility is that h(x) is a vertical shift of f(x) by 2 units down.
The answer to 1) is option C.
2) In general, a vertical shift has the form g(x)->g(x)+d (d units up if d>0 and vice-versa).
Therefore, in our case,
[tex]h(x)=f(x)-2=x^3-2[/tex]
The answer is x^3-2, option A.
