Describe the transformations from the parent function f(x)=x^3 g(x)=-3(x-4)^3-5

To describe the transformations from the parent function $f(x)=x^{3}$ to the function $g(x)=-3(x-4)^{3}-5$, we need to analyze the changes in the equation.<br /><br />1. Horizontal shift:<br />The term $(x-4)$ in the function $g(x)$ indicates a horizontal shift of the graph of $f(x)$ to the right by 4 units.<br /><br />2. Vertical stretch and reflection:<br />The coefficient $-3$ in front of the cubic term in $g(x)$ indicates a vertical stretch by a factor of 3 and a reflection across the x-axis.<br /><br />3. Vertical shift:<br />The constant term $-5$ in $g(x)$ indicates a vertical shift of the graph of $f(x)$ downward by 5 units.<br /><br />Therefore, the transformations from the parent function $f(x)=x^{3}$ to the function $g(x)=-3(x-4)^{3}-5$ are:<br />- Horizontal shift to the right by 4 units<br />- Vertical stretch by a factor of 3<br />- Reflection across the x-axis<br />- Vertical shift downward by 5 units