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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As you know john locke said he wanted life liberty and the pursuit of happiness so thomas jefferson was inspired about what john locke said so thomas jefferson wrote the declaration of independence for people to be free for people to be happy

  b.   the average rate of change of f(x) is less than the average rate of change of g(x).

step-by-step explanation:

since the length of the interval is the same in each case, we only need to compare the change in y-value to see which is greater.

f(-2) = -3f(1) = 6 . . . estimated from f(x) = (x+2)^2-3, which matches points on the graph (-1,-2) and (0, 1)

so the change in y-value for function f is (6 )) = 9.

the table tells us

g(-2) = 1g(1) = 31

so the change in y-value for function g is (31 -1) = 30.

the change in y-value of f(x) on the interval is less than the change in y-value of g(x) on the same interval, so the average rate of change of f(x) is less than the average rate of change of g(x).