Problem 1
Answer: choice C) f(x) = (-1/2)cos(x)
We can rule out anything with sine in it since the graph does not go through the origin. We can rule out choice A as well since plugging x = 0 into f(x) leads to a positive result, when instead we want a negative value. So the only thing left is choice C
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Problem 2
See the attached image
Point A is approximately (1.57, 0) which is exactly (pi/2, 0)
Point B is approximately (3.14, -2) which is exactly (pi, -2)
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Problem 3
Answer: 1/pi
Period = pi since the graph repeats itself every pi units
Frequency = 1/Period
Frequency = 1/pi
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Problem 4
Answer: Choice A) f(x) = cos(2x)
This is a cosine function as it doesn't go through the origin. The period is T = pi, so b = 2pi/T = 2pi/pi = 2 is the coefficient of the inner x term. Therefore the function is f(x) = cos(2x)
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