Question

Which transformations are needed to change the parent cosine function to y=3 cos(10(x-3.14))

Answer 1

y=cos(x)===>y = 3 cos (10x-31.4) = 3 cos (10(x-3.14)) First of all, the three in front of "cos" tells us that we must stretch cos(x), or expand, vertically by 3. After that, the 10 inside "cos" tells us that we now need to compress horizontally by 10. Finally, the "x-3.14" tells us that we need to move right by units, but it doesn't really matter, because the graph still looks exactly the same after moving right 3.14 units. Summary: Expand vertically by 3Compress horizontally by 10Move right 3.14 units

Answer 2

y=cos(x)
===>
y = 3 cos (10x-31.4) = 3 cos (10(x-3.14))

First of all, the three in front of "cos" tells us that we must stretch cos(x), or expand, vertically by 3. After that, the 10 inside "cos" tells us that we now need to compress horizontally by 10. Finally, the "x-3.14" tells us that we need to move right by
`\pi`units, but it doesn't really matter, because the graph still looks exactly the same after moving right 3.14 units.

Summary:
Expand vertically by 3
Compress horizontally by 10
Move right 3.14 units