Question

Which equation defines the graph of y=x^3 after it is shifted vertically 5 units down and horizontally 4 units to the left?
y=(x+4)^3-5 is the answer because show work

Answer 1

To shift the graph of y=x^3 horizontally 4 units to the left, we need to replace x with (x+4) in the equation. This is because when x is decreased by 4 units, (x+4) will equal the original value of x.

Similarly, to shift the graph vertically 5 units down, we need to subtract a constant value of 5 from the equation.

Therefore, the equation that defines the graph of y=x^3 after it is shifted vertically 5 units down and horizontally 4 units to the left is:

y = (x+4)^3 - 5