Write an equation for a function with the given characteristics. a cosine curve with a period of pi, and amplitude of 1, a left phase shift of pi, and vertical transiation up 5/2 of a unit.

y = cos (2x + 2π) - 5/2

Step-by-step explanation:

y = a cos (bx + c) +d

a = Amplitude =1

period = 2π/b =π

b= 2

phase shift  c/b = π

c/2 =π

c =2π

vertical translation = 5/2 units

d = -5/2 downwards

therefore substituting the values

y=1 cos (2x +2π) - 5/2

y = cos (2x + 2π) - 5/2  ;equation  for the function

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a reflection across the x-axis , followed by the by a reflection across the y-axis , and then a scale dilation of 0.5 .