Find the equation of a cosine curve that is obtained by shif

Find the equation of a cosine curve that is obtained by shifting the graph of y=cos(x)
- to the left 6 units and
- upward 3 units and
- vertically compressed by a factor of 8 and
- vertically flipped

Solution

y=cos(x)

-shifting to the left 6 units

=>y=cos(x+6)

- upward 3 units

=>y=3+cos(x+6)

- vertically compressed by a factor of 8

=>y=(1_/8)(3+cos(x+6))

- vertically flipped

=>y= -(1_/8)(3+cos(x+6))