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

Respuesta :

Answer:

[tex]f(x)=\frac{1}{2}Cos(\frac{1}{4}x)-1[/tex]

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

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Answer:

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