Modeling with Periodic Functions

Question 1

The first decision is a choice between y = acos[b(x – h)] + k and y = asin[b(x – h)] + k.Starting at the green point, which general pattern does the graph follow? mid-max-mid-min-midmid-min-mid-max-midmax-mid-max-mid-minmin-mid-max-mid-min

Revolt · Accepted Answer

mid-max-mid-min-mid

Question 2

The pattern is that of cosinesine–cosine–sine.

Revolt · Accepted Answer

sine

Question 3

Recall that h, the phase shift, is any value of x that occurs at the beginning of a cycle. The green point begins the –cosine cycle. What value of x corresponds to this point?h = [___]

Revolt · Accepted Answer

pi

Question 4

The vertical shift, k, is the amount every y-value is shifted when compared to the basic sine or cosine function. In other words, it is the same y-value as the midline. For the equation of this graph, k = [___].

Revolt · Accepted Answer

2

Question 5

The y-value for the midline is equal to max y + min y(max y + min y)/2max y – min y(max y – min y)/2.

Revolt · Accepted Answer

(max y + min y)/2

Question 6

What is the amplitude of this graph?[___]

Revolt · Accepted Answer

2

Question 7

The formula for period is StartFraction 2 pi Over b EndFraction . Use the value of the period, 2.244, to solve for the value of b, rounded to the nearest tenth:b =

Revolt · Accepted Answer

2.8

Question 8

The period is .

Revolt · Accepted Answer

2.244

Modeling with Periodic Functions Answers

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