Explain the transformations that have taken place

Question

Explain the transformations that have taken place for the function g(x)=cosx to become the function h(x)=-2cos(pi*x + pi/4).

 

-reflected in the x axis

-stretched vertically by a factor of 2

- shifted 1/4 to the left

 

I know the period is now 2 but I'm not sure what factor it has been shrunk horizontally by :/ 

Answer 1

it's been stretched vertically by a factor of 2

it used to have amplitude of 1. now it has amplitude of 2

horizontally, the period shrunk from 2pi to 2, it shrunk by a factor of pi

compare the changes in Acos(Bx -C) + D

from cosx to 2cos(pix + pi/4)'= 2cos(pi(x + 1/4)

phase shift is -1/4, shift to the left by 1/4