Question

Which transformations are needed to change the parent cosine function to
y = 0.35cos(8(x-pi/4))

Answer 1

Here's a list of the changes and their effect:

$\begin{array}{c|c|c}\text{From}&\text{To}&\text{Effect}\\\cos(x)&\cos\left(x-\frac{\pi}{4}\right)&\text{Horizontal shift}\\\cos\left(x-\frac{\pi}{4}\right)&\cos\left(8\left(x-\frac{\pi}{4}\right)\right)&\text{Horizontal compression}\\\cos\left(8\left(x-\frac{\pi}{4}\right)\right)&0.35\cos\left(8\left(x-\frac{\pi}{4}\right)\right)&\text{Vertical compression}\end{array}$

So, the function is shifted $\frac{\pi}{4}$ units to the right, then it is compressed by a factor 8 horizontally, and a factor 0.35 vertically.

Answer 2

Answer:

C:  vertical compression of 0.35, horizontal compression to a period of pi/4, phase shift of pi/4 units to the right

Step-by-step explanation: