SOLUTION: If f(x) = cosx, write a function g(x) for the sinusoid that translates f(x) with the following transformations:
Reflected over the midline y=-3, with an amplitude of 3, twice th
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Question 1115522: If f(x) = cosx, write a function g(x) for the sinusoid that translates f(x) with the following transformations:
Reflected over the midline y=-3, with an amplitude of 3, twice the period, and a phase shift of pi/2 to the right.
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!
The general cosine function is
a is the amplitude;
b determines the period (the period is 2pi/b);
c is the horizontal phase shift; and
d is the vertical shift.
"reflected..." -- that means a is negative
"...over the midline y=3..." -- that's a vertical shift; d is 3
"...with an amplitude of 3..." -- we already know a is negative; now this means a is -3
"...twice the period..." -- the period is 4pi; since the period is 2pi/b, b is 1/2
"...and a phase shift of pi/2 to the right -- that means c is pi/2
Put it all together, using the values of a, b, c, and d you have determined:
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