Question

I need help with these 1&3 there one whole answer

Answer 1

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

$\begin{gathered} (0,0)\rightarrow(2,0) \\ (0,0)\rightarrow(-0,0)=(0,0) \\ (0,0)\rightarrow(0,-2) \\ (0,0)\rightarrow(0,2*0)=(0,0) \end{gathered}$

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,

$h(x)=f(x)-2=x^3-2$

The answer is x^3-2, option A.