QuestionIdentify the parent function for $f(x)=\frac{2}{3}(x-8)^{3}$ and its transformations: reflections, stretches, vertical shifts, horizontal shifts.

Studdy Solution
Since the value of $a$ is positive, there is no reflection over the x-axis. And since the function is not written in the form $y=a(-x)^{3}$, there is no reflection over the y-axis. So, the correct transformation for Reflections is "No reflection".
In conclusion, the parent function is $y=x^{3}$, and the transformations applied are a vertical compression by a factor of $\frac{2}{3}$, a shift to the right by units, and no reflection or vertical shift.