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i don't know how to do this :(

 May 3, 2022
 #1
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The absolute value of the amplitude is the coefficient of sin or cos, so either \(f(x) = 2 \cos(\boxed{\phantom{ aaaa }}x)+\boxed{\phantom{ aaaa }}\) or \(f(x) = -2 \cos(\boxed{\phantom{ aaaa }}x)+\boxed{\phantom{ aaaa }}\). Since it is the reflection of its parent function g(x) = cos(x) over x-axis, we determine that it must be \(f(x) = -2 \cos(\boxed{\phantom{ aaaa }}x)+\boxed{\phantom{ aaaa }}\)

 

Vertical shift is the constant term, but you need to consider the direction of the shift. Shifting downwards means a negative constant term, so \(f(x) = -2 \cos(\boxed{\phantom{ aaaa }}x)-11\).

 

We also know that the period of \(h(x) = a \cos (bx + c) + d \) is \(\dfrac{2\pi}b\). You can solve the equation \(\dfrac{2\pi}b = \dfrac{6\pi}7\) to get the remaining blank.

 May 3, 2022

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