Modeling with Periodic Functions — Unit test

Question 1

Which function is the same as ?

Revolt · Accepted Answer

y = negative 3 sine (2 (x + StartFraction pi Over 4 EndFraction)) minus 2

Question 2

Which of the following is the equation of the function below?

Revolt · Accepted Answer

y equal to 2 secant left-square-bracket 2 (x + pi) right-square-bracket minus 2.

Question 3

Which transformations are needed to change the parent sine function to the sine function below?

Revolt · Accepted Answer

vertical compression of , horizontal stretch to a period of , vertical shift of 1 unit up, phase shift of units left

Question 4

Which point does the graph of the parent function pass through?

Revolt · Accepted Answer

(StartFraction pi over 3 EndFraction , square root of 3)

Question 5

What is the general equation of a sine function with an amplitude of 6, a period of , and a horizontal shift of ?

Revolt · Accepted Answer

y = 6 sine (8 (x minus StartFraction pi Over 2 EndFraction))

Question 6

Which of the following is the equation of the function below?

Revolt · Accepted Answer

y equal to 2 secant left-square-bracket 2 (x plus StartFraction pi over 6 EndFraction) plus 2.

Question 7

The depth of the water at the end of a pier changes periodically along with the movement of tides. On a particular day, low tides occur at 12:00 a.m. and 3:30 p.m., with a depth of 3.25 meters, while high tides occur at 7:45 a.m. and 11:15 p.m., with a depth of 8.75 meters. Which of the following equations models d, the depth of the water in meters, as a function of time, t, in hours? Let t = 0 be 12:00 a.m.

Revolt · Accepted Answer

d = negative 2.75 cosine (StartFraction 4 pi Over 31 EndFraction t) + 6

Question 8

The average daily temperature, t, in degrees Fahrenheit for a city as a function of the month of the year, m, can be modeled by the equation , where m = 0 represents January 1, m = 1 represents February 1, m = 2 represents March 1, and so on. Which equation also models this situation?

Revolt · Accepted Answer

t = negative 35 sine (StartFraction pi Over 6 EndFraction m) + 55

Question 9

The height, h, in feet of a ball suspended from a spring as a function of time, t, in seconds can be modeled by the equation . What is the height of the ball at its equilibrium?

Revolt · Accepted Answer

k feet

Question 10

What is the domain of the function ?

Revolt · Accepted Answer

all real numbers except , where n is any integer

Modeling with Periodic Functions — Unit test Answers

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