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

Answer:

$f(x)=\frac{1}{2}Cos(\frac{1}{4}x)-1$

Step-by-step explanation:

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

• The function f(x) = $\frac{1}{a}$ cos x is a vertical compression of the original by a factor of a
• The function f(x) = cos $(\frac{1}{b}x)$ 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) = $\frac{1}{2}Cos(\frac{1}{4}x)-1$

Answer 2

Answer:

Hope this helps :)

Step-by-step explanation: