Which transformations are needed to change the parent cosine function to y = 3 cosine (10 (x minus pi)) ? vertical compression of 3, horizontal stretch to a period of 5 pi, phase shift of pi units to the left vertical stretch of 3, horizontal compression to a period of StartFraction pi Over 5 EndFraction, phase shift of Pi units to the right vertical compression of 3, horizontal stretch to a period of 10p, phase shift of Pi units to the right vertical stretch of 3, horizontal compression to a period of StartFraction pi Over 5 EndFraction, phase shift of Pi units to the left

Question

Chemistry

Conrad

14 July, 19:12

Which transformations are needed to change the parent cosine function to y = 3 cosine (10 (x minus pi)) ? vertical compression of 3, horizontal stretch to a period of 5 pi, phase shift of pi units to the left vertical stretch of 3, horizontal compression to a period of StartFraction pi Over 5 EndFraction, phase shift of Pi units to the right vertical compression of 3, horizontal stretch to a period of 10p, phase shift of Pi units to the right vertical stretch of 3, horizontal compression to a period of StartFraction pi Over 5 EndFraction, phase shift of Pi units to the left

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Answers (1)

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Hodges · Answer 1

vertical stretch of 3, horizontal compression to a period of π/5, phase shift of π units to the right

Explanation:

The parent function f (x) = cos (x) has been transformed to ...

y = A·f ((2π/B) (x - C))

where A = 3, B = π/5, C = π

In this form, A is the vertical stretch factor, B is the period, and C is the right shift.

The function has been ...

vertically stretched by a factor of 3 horizontally compressed to a period of π/5 right shifted by π

This collection of transformations matches the 2nd choice in this list.