Respuesta :

semsee45

Answer:

Amplitude = 1/2

Period  =  [tex]\dfrac23 \pi[/tex]

Phase shift = [tex]\pi[/tex] (left)

Vertical shift = [tex]-3[/tex]

Step-by-step explanation:

[tex]f(x)=-\dfrac12cos(3(x+\pi))-3[/tex]

[tex]y = A sin(B(x + C)) + D[/tex]

Amplitude is A = 1/2

Period  is [tex]\dfrac2B \pi[/tex] =  [tex]\dfrac23 \pi[/tex]

Phase shift is C= [tex]\pi[/tex] (left)

Vertical shift is D = [tex]-3[/tex]

The form is

[tex]\\ \tt\longmapsto f(x)=Asin(B(x+c))+D[/tex]

where

  • A=Amplitude
  • Period=2π/B
  • Phase shift=c
  • Vertical shift=D

Now compare to our given function

  • Amplitude=-1/3
  • Period=2π/3
  • phase shift=c=π
  • Vertical shift=-3

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