Question

the graph of f(x) shown below has the same shape as the graph of g(x)=x^4 but it is shifted to the right 1 unit what is its equation

Answer 1

What you must do for this problem is to re-imagine the equation in "vertex form"

Vertex form: $y=a(x-h)^{2} +k$
where "h" shifts the graph to the right if "h" is positive" and to the left if "h" is negative. K shifts the graph up and down.

$g(x)=a(x-h)^{2} +k$
$g(x)=1(x-1)^{4} +0$
a=1
h=1
k=0

So, your final answer should be: $g(x)= (x-1)^{4}$