For this case we have to define function transformation that:
Let k> 0:
To graph [tex]y = f (x) + k,[/tex] the graph is displayed k units up.
To graph[tex]y = f (x) -k[/tex], the graph is displayed k units units down.
Let h> 0:
To graph[tex]y = f (x-h)[/tex], the graph moves units to the right.
To graph [tex]y = f (x + h)[/tex], the graph moves h units to the left.
We have [tex]y = - \sqrt [3] {x}[/tex]
It moves 7 units up and 4 to the right.
So we have to:
[tex]h = 4\\k = 7[/tex]
The shifted graphic is:
[tex]y = - \sqrt [3] {x-4} +7[/tex]
ANswer:
[tex]y = - \sqrt [3] {x-4} +7[/tex]
