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Consider the cubic function g(x)=-2(x+4)^3-5. Please describe how this function has been transformed from the cubic parent function f(x)=x^3

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Answer: The cubic parent function f(x)=x^3 has been transformed to form the function g(x)=-2(x+4)^3-5 in the following ways:

Vertical scaling: The function has been vertically scaled by a factor of -2, which means that the height of the function has been multiplied by -2.

Horizontal shift: The function has been horizontally shifted 4 units to the right. This is because the expression inside the parenthesis (x+4) can be seen as shifting the graph 4 units to the right.

Vertical shift: The function has been vertically shifted down by 5 units. This is because the constant term -5 has been added to the expression, which moves the graph down by 5 units.

So, the parent function f(x)=x^3 has been transformed by a vertical scaling by -2, followed by a horizontal shift 4 units to the right, and finally a vertical shift 5 units down to form the function g(x)=-2(x+4)^3-5.

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