Answer: OPTION D.
Step-by-step explanation:
Below are some transformations for a function f(x):
If
, then the function is reflected over the x-axis.
If
, then the function is reflected over the y-axis.
If
and
, then the function is horizontally compressed.
If
and
, then the function is horizontally stretched.
In this case you know that the parent function is:
![y=x^3](https://tex.z-dn.net/?f=y%3Dx%5E3)
According to the information given in the exercise, the parent function IS horizontally stretched by a factor of
and it is also reflected over the y-axis.
Therefore, based on the transformations explained before, you can notice that the transformation is:
Where ![0 < b](https://tex.z-dn.net/?f=0%20%3C%20b%20%3C1)
Therefore, the equation of the transformed function is:
![y=(-\frac{1}{5}x)^ 3](https://tex.z-dn.net/?f=y%3D%28-%5Cfrac%7B1%7D%7B5%7Dx%29%5E%203)