Write the function whose graph is the graph of y=x3, but is shifted down 2 units.

Let the original function be .

This function produces values like (x, f(x)): (1, 1), (2, 8), (5, 125), etc...

Shifting the function down means that the y-values 1, 8, 125 become respectively:

1-2=-1

8-2=6

125-2=123.

These examples illustrate that to shift the graph 2 units down, we need to subtract 2 from f(x).

Thus, a function whose graph is that of f(x) shifted 2 units down is y=f(x)-2.

 

I'm sure the answer is a