Question

How does the graph of g(x) = (x + 2)3 − 7 compare to the parent function of f(x) = x3?

Answer 1

shifted 2 to the left and 7 down

Explanation:

Answer 2

• The graph of g(x) is a shift of the graph of f(x) 2 units left and 7 units down.

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:

`f(x)=x^3`

and the transformed function g(x) as:

`g(x)=(x+2)^3-7\\\\i.e.\\\\g(x)=f(x+2)-7`

Hence, the shift is 2 units to the left and 7 units down.