Respuesta :
Answer:
- The graph of g(x) is a shift of the graph of f(x) 2 units left and 7 units down.
Step-by-step explanation:
We know that the transformation of the parent function f(x) to f(x+a) is a shift of the function f(x) a units to the left or to the right depending on a.
if a>0 then the shift is a units to the left.
and if a<0 then the shift is a units to the right.
Also the transformation of the type:
f(x) to f(x)+k
is a shift of the function f(x) k units up or down depending on k.
if k>0 then the shift is k units up.
and if k<0 then the shift is k units down.
Here we have the parent function f(x) as:
[tex]f(x)=x^3[/tex]
and the transformed function g(x) as:
[tex]g(x)=(x+2)^3-7\\\\i.e.\\\\g(x)=f(x+2)-7[/tex]
Hence, the shift is 2 units to the left and 7 units down.
