For this case we have:
Let k> 0:
To graph[tex]y = f (x) + k,[/tex] the graph k units is moved up.
To graph [tex]y = f (x) -k[/tex], the graph moves k units down.
Let h> 0:
To graph [tex]y = f (x-h)[/tex], the graph moves h units to the right.
To graph [tex]y = f (x + h),[/tex] the graph moves h units to the left.
So, we have:
[tex]y = f (x) = \sqrt [3] {x}[/tex]
Shifted 1 unit down and 4 to the left means:
[tex]k = 1\\h = 4[/tex]
[tex]y = f (x) = \sqrt [3] {x + 4} -1[/tex]
Answer:
Option D
