Let the original function be [tex]\displaystyle{ f(x)=x^3[/tex].
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.
Answer: [tex]y=x^3-2[/tex]
