which transformations are needed to change the parent cosine function to (y = 0.35cosleft8left(x-\frac{pi}{4}…

which transformations are needed to change the parent cosine function to (y = 0.35cosleft8left(x-\frac{pi}{4}\right)\right)?\nvertical stretch of 0.35, horizontal stretch to a period of (16pi), phase shift of (\frac{pi}{4}) units to the right\nvertical compression of 0.35, horizontal compression to a period of (4pi), phase shift of (\frac{pi}{4}) units to the left\nvertical compression of 0.35, horizontal compression to a period of (\frac{pi}{4}), phase shift of (\frac{pi}{4}) units to the right\nvertical stretch of 0.35, horizontal stretch to a period of (\frac{pi}{4}), phase shift of (\frac{pi}{4}) units to the right

which transformations are needed to change the parent cosine function to (y = 0.35cosleft8left(x-\frac{pi}{4}\right)\right)?\nvertical stretch of 0.35, horizontal stretch to a period of (16pi), phase shift of (\frac{pi}{4}) units to the right\nvertical compression of 0.35, horizontal compression to a period of (4pi), phase shift of (\frac{pi}{4}) units to the left\nvertical compression of 0.35, horizontal compression to a period of (\frac{pi}{4}), phase shift of (\frac{pi}{4}) units to the right\nvertical stretch of 0.35, horizontal stretch to a period of (\frac{pi}{4}), phase shift of (\frac{pi}{4}) units to the right

Answer

Answer:

vertical compression of 0.35, horizontal compression to a period of $\frac{\pi}{4}$, phase shift of $\frac{\pi}{4}$ units to the right

Explanation:

Step1: Analyze vertical transformation

The coefficient 0.35 in front of cosine compresses the parent - cosine function vertically since $0 < 0.35<1$.

Step2: Recall period formula

The period of the parent cosine function $y = \cos(x)$ is $2\pi$. For the function $y = A\cos(B(x - C))$, the period $T=\frac{2\pi}{B}$. Here $B = 8$, so $T=\frac{2\pi}{8}=\frac{\pi}{4}$, which is a horizontal compression.

Step3: Determine phase - shift

For the function $y = A\cos(B(x - C))$, the phase - shift is given by $C$. Here $C=\frac{\pi}{4}$, and a positive $C$ value means a shift to the right.