Question

The graph of the parent function y = x cubed is horizontally stretched by a factor of One-fifth and reflected over the y-axis. What is the equation of the transformed function?
A.) y = (5 x) cubed
B.)y = (negative 5 x) cubed
C.)y = (one-fifth x) cubed
D.)y = (negative one-fifth x) cubed

Answer 1

Answer: OPTION D.

Step-by-step explanation:

Below are some transformations for a function f(x):

If $-f(x)$, then the function is reflected over the x-axis.

If $f(-x)$, then the function is reflected over the y-axis.

If $f(bx)$  and $b>1$, then the function is horizontally compressed.

If  $f(bx)$  and $0 < b$, then the function is horizontally stretched.

In this case you know that the parent function is:

$y=x^3$

According to the information given in the exercise, the parent function IS horizontally stretched by a factor of $\frac{1}{5}$ and it is also reflected over the y-axis.

Therefore, based on the transformations explained before, you can notice that the transformation is:

$f(-bx)$

Where $0 < b$

Therefore, the equation of the transformed function is:

$y=(-\frac{1}{5}x)^ 3$

Answer 2

Answer:

its D on edu

Step-by-step explanation: