Using translation concepts, it is found that the equation that represents the new function is:
- [tex]y = -3\sqrt[3]{x} - 8[/tex]
The cube root parent function is given by:
[tex]y = \sqrt[3]{x}[/tex]
Translation:
The function goes through these following translations:
- Vertically stretched by a factor of 3, that is, it is multiplied by 3, hence [tex]y = 3\sqrt[3]{x}[/tex].
- Reflected over the x-axis, that is, it is multiplied by -1, hence [tex]y = -3\sqrt[3]{x}[/tex].
- Translated 8 units down, that is, 8 is subtracted from the function, hence [tex]y = -3\sqrt[3]{x} - 8[/tex].
Then, the equation is:
- [tex]y = -3\sqrt[3]{x} - 8[/tex]
To learn more about translation concepts, you can take a look at https://brainly.com/question/13671886
