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