1. picture
2.picture
3.which graph represents f(x)=4sin(2πx)?
4. a cosine function has a period of 3, a maximum value of 20, and a minimum value of 0. the function is a reflection of its parent function over the x-axis.
which function could be the function described?
5. a sinusoidal function whose frequency is 3, maximum value is 15, minimum value is −3 has a y-intercept of 6.
which function could be the function described?
f(x)=9sin(6πx)+3
f(x)=9sin(3x)+3
f(x)=9sin(x3)+6
f(x)=9sin(6πx)+6

Problem 1

See the attached image. Specifically see figure 1.

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Problem 2

See the attached image. Specifically see figure 2.

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Problem 3

bottom right corner

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f(x) = 4*sin(2pi*x)
f(x) = a*sin(b*x)
a = 4 is the amplitude
b = 2pi
T = 2pi/b = 2pi/2pi = 1 is the period

The graph that has a period of 1 and amplitude 4 is the bottom row of choices. We can rule out the graph on the left because sine starts off increasing as you move away from the origin and go from left to right. 

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Problem 4

f(x) = -10cos(2pi*x/3)

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T = period = 3
b = 2pi/T = 2pi/3
amplitude = (max - min)/2
amplitude = (20-0)/2
amplitude = 10
y = 10 is the midline since d = (20+0)/2 = 10

f(x) = a*cos(bx)+d
f(x) = -10*cos(2pi*x/3)+10

Note: the value of 'a' is negative because of the reflection over the x axis
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Problem 5

Choice D
f(x) = 9*sin(6pi*x)+6

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min = -3
max = 15
midline: d = (max + min)/2 = (15-3)/2 = 6
amplitude: a = (max - min)/2 = (15+3)/2 = 9
f = frequency = 3
T = period = 1/f = 1/3
b = 2pi/T = 2pi/(1/3) = 6pi

f(x) = a*sin(bx)+d
f(x) = 9*sin(6pi*x)+6

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