Describe the transformations

Question

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

 

Answer 1

g(x) = cosx

 

h(x) = -2cos((x + 1/4)π)

 

 

 

First, g(x) was shifted 1/4 units to the left with a vertical stretch.

 

Then, g(x) was stretch vertically by a scale factor of 2.  We know this because the amplitude went from 1 to 2.

 

Then, g(x) was reflected about the x-axis.