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# stumped!!

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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