Given the cubic function h(x)=5(x-2)^3-13 Choose each of the following that represents the transformations of the parent function. Translated 2 units square and translated 13 square and a vertical square by a factor of 5

To analyze the transformations of the cubic function \( h(x) = 5(x-2)^3 - 13 \), we need to compare it with the parent function \( f(x) = x^3 \).<br /><br />1. **Horizontal Translation**: The expression \( (x-2) \) indicates a horizontal translation. Specifically, it translates the graph 2 units to the right.<br /><br />2. **Vertical Translation**: The term \(-13\) at the end of the function indicates a vertical translation. It translates the graph 13 units downward.<br /><br />3. **Vertical Stretch**: The coefficient 5 in front of \((x-2)^3\) indicates a vertical stretch by a factor of 5.<br /><br />Therefore, the transformations are:<br />- Translated 2 units **right**<br />- Translated 13 units **downward**<br />- A vertical **stretch** by a factor of 5