Question

write the equation for the cosine function that has been compressed vertically by a factor of 2, stretched horizontally by a factor of 4, and shifted down one unit

Answer 1

Hope this helps :)

Explanation:

Answer 2

`f(x)=(1)/(2)Cos((1)/(4)x)-1`

Explanation:

Consider the function f(x) = cos x. Noted below are the points of transformations of the cos function

• The function f(x) =
  `(1)/(a)` cos x is a vertical compression of the original by a factor of a
• The function f(x) = cos
  `((1)/(b)x)` is a horizontal stretch of the original function by a factor b
• The function f(x) = cosx - c is the original function shifted down c units

Considering the points above, we can now write down the "transformed" cosine function's equation:

f(x) =
`(1)/(2)Cos((1)/(4)x)-1`