Question

Which transformations are needed to change the parent cosine function to the cosine function below?

On a coordinate plane, a curve crosses the y-axis at y = 1. It has a maximum of 1 and a minimum of negative 3. It goes through 2 cycles at 2 pi.

vertical stretch of 2, horizontal stretch to a period of 2 pi, phase shift of StartFraction pi Over 2 EndFraction units to the right, vertical shift of 1 unit up

vertical compression of 2, horizontal stretch to a period of StartFraction pi Over 4 EndFraction, phase shift of StartFraction pi Over 4 EndFraction units to the left, vertical shift of 2 units down

vertical compression of 2, horizontal compression to a period of 4 pi, phase shift of StartFraction pi Over 3 EndFraction units to the left, vertical shift of 1 unit down

vertical stretch of 2, horizontal compression to a period of StartFraction pi Over 2 EndFraction, phase shift of Pi units to the right, vertical shift of 1 unit down

Answer 1

vertical stretch of 2, horizontal compression to a period of StartFraction pi Over 2 EndFraction, phase shift of Pi units to the right, vertical shift of 1 unit down

Explanation:

Answer 2

vertical stretch of 2, horizontal compression to a period of StartFraction pi Over 2 EndFraction, phase shift of Pi units to the right, vertical shift of 1 unit down

Explanation:

If you stretch cosine function by a factor of 2, maximum will be y = 2 and minimum will be y = -2, and after that you shift it 1 unit down maximum will be y = 1 and minimum will be y = -3