Answer:
Option D
The function shifted vertically 5 units down and horizontally left 4 units is, [tex]y=(x+4)^3-5[/tex]
Step-by-step explanation
The function is given by, y=[tex]f(x)=x^3[/tex]
To move a function shift vertically 5 units down
We know that moving the function down, you subtract outside the function i.e, [tex]f(x)-c[/tex]; [tex]f(x)[/tex] moved down c units.
Therefore, the function f(x) vertically shift 5 units down by [tex]f(x)=x^3-5[/tex]
Now, to move a function horizontally 4 units left.
To shift the function left add inside the function's argument i.e, [tex]f(x+a)[/tex] gives f(x) shifted a units to the left.
so, the function f(x) horizontally left 4 units i.e, f(x+4)=[tex](x+4)^3[/tex]
Now, the graph of the function [tex]y=x^3[/tex] after it is shifted vertically 5 units down and horizontally left 4 units is, [tex]y=(x+4)^3-5[/tex]
