Question

The graphs below have the same shape. What is the equation of the blue graph? Picture below

Answer 1

check the picture below.

Answer 2

we have that

$f(x)=x^{3}$

we know that

$A(0,0)-------> A'(3,0)$

the rule of the translation is

$(x,y)-----> (x+3,y)$

that means

the translation is $3$ units to the right

so

the equation of g(x) is

$g(x)=(x-h)^{3}$

where

$h=3\ units$

substitute

$g(x)=(x-3)^{3}$

therefore

the answer is

$g(x)=(x-3)^{3}$