Answers Algebra 2 MP 234 CHSModeling with Periodic Functions

Absolute Value Functions Answers

17 verified answers2 views

Free Preview

Which of the following could be the equation of the function below?

y = 0.5 cosine (2 (x minus StartFraction pi Over 2 EndFraction)) + 2

y = 0.5 cosine (4 (x minus StartFraction pi Over 2 EndFraction)) minus 2

y = 0.5 cosine (4 (x + pi)) + 2

y = 0.5 cosine (2 (x minus pi)) minus 2

Free Preview

Which function describes the graph below?

f (x) = 6 cosine (x)

f (x) = 3 cosine (x) + 3

f (x) = 6 sine (x)

f (x) = 3 sine (x) + 3

The height, h, in feet of the tip of the hour hand of a wall clock varies from 9 feet to 10 feet. Which of the following equations can be used to model the height as a function of time, t, in hours? Assume that the time at t = 0 is 12:00 a.m.

h = 0.5 cosine (StartFraction pi Over 12 EndFraction t) + 9.5

h = 0.5 cosine (StartFraction pi Over 6 EndFraction t) + 9.5

h = cosine (StartFraction pi Over 12 EndFraction t) + 9

h = cosine (StartFraction pi Over 6 EndFraction t) + 9

The blades of a windmill turn on an axis that is 30 feet from the ground. The blades are 10 feet long and complete 2 rotations every minute. Write a sine model, y = asin(bt) + k, for the height (in feet) of the end of one blade as a function of time t (in seconds). Assume the blade is pointing to the right when and that the windmill turns counterclockwise at a constant rate.

y = 30 sine (StartFraction pi Over 15 EndFraction t) + 10

y = 30 sine (StartFraction pi Over 15 EndFraction t) + 30

y = 10 sine (StartFraction pi Over 15 EndFraction t) + 10

y = 10 sine (StartFraction pi Over 15 EndFraction t) + 30

What is the equation of the graph below?

y = sine (x + 90 degrees)

y = cosine (x + 90 degrees)

y = sine (x + 45 degrees)

y = cosine (x + 45 degrees)

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

y equal to 2 cosecant left-square-bracket 0 point 5 (x plus StartFraction pi over 2 EndFraction) right-square-bracket minus 1.

y equal to 2 cosecant left-square-bracket 2 (x plus StartFraction pi over 4 EndFraction) minus 1 right-square-bracket.

y equal to 0 point 5 cosecant left-square-bracket 0 point 5 (x plus StartFraction pi over 2 EndFraction) right-square-bracket minus 1.

y equal to 0 point 5 cosecant left-square-bracket 2 (x plus StartFraction pi over 4 EndFraction) right-square-bracket minus 1.

The blades of a windmill turn on an axis that is 35 feet above the ground. The blades are 10 feet long and complete two rotations every minute. Which of the following equations can be used to model h, the height in feet of the end of one blade, as a function of time, t, in seconds? Assume that the blade is pointing to the right, parallel to the ground at t = 0 seconds, and that the windmill turns counterclockwise at a constant rate.

h = negative 10 sine (StartFraction pi Over 15 EndFraction t) + 35

h = negative 10 sine (Pi t) + 35

h = 10 sine (StartFraction pi Over 15 EndFraction t) + 35

h = 10 sine (Pi t) + 35

Which of the following is the graph of y = cos(2x)?

mc008-1.jpg

mc008-2.jpg

mc008-3.jpg

mc008-4.jpg

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 . Which of the following is the graph of this equation?

On a coordinate plane, a curve crosses the y-axis at (0, 5). It increases to (2, 8), and then decreases to (6, 2).

On a coordinate plane, a curve crosses the y-axis at (0, 8). It decreases to (4, 2), and then increases to (8, 8).

On a coordinate plane, a curve crosses the y-axis at (0, 5). It increases to (1, 8), and then decreases to (3, 2).

On a coordinate plane, a curve crosses the y-axis at (0, 5). It decreases to (2, 1), and then increases to (3, 8).

What is the period of the function ?

units

Which of the following is the graph of ?

On a coordinate plane, the x axis ranges from negative 2 pi to 2 pi with an interval of pi units and the y axis ranges from negative 5 to 1 with an interval of 1 unit. The graph is 2 pi periodic with asymptotes at x equals plus or minus n pi. It touches the lines y equals negative 3 by 2 at (3 pi by 2, comma negative 3 by 2 ) and (negative pi by 2 by negative 3 by 2) and y equals negative 5 by 2 at ( pi by 2 comma negative 5 by 2) and (negative 3 pi by 2 comma negative 5 by 2).

On a coordinate plane, the x axis ranges from negative 2 pi to 2 pi with an interval of pi units and the y axis ranges from negative 5 to 1 with an interval of 1 unit. The graph is 2 pi periodic with asymptotes at x equals plus or minus n pi. It touches the lines y equals negative 1 at (3 pi by 2 comma negative 1) and (negative pi by 2 comma negative 1) and y equals negative 3 at (pi by 2 comma negative 3) and (negative 3 pi by 2 comma negative 3).

On a coordinate plane, the x axis ranges from negative 2 pi to 2 pi with an interval of pi units and the y axis ranges from negative 5 to 1 with an interval of 1 unit. The graph is 2 pi periodic with asymptotes at x equals plus or minus n pi. It touches the lines y equals negative 1 at (pi comma negative 1) and (negative pi comma negative 1) and y equals negative 3 at (0 comma negative 3).

On a coordinate plane, the x axis ranges from negative 2 pi to 2 pi with an interval of pi units and the y axis ranges from negative 5 to 1 with an interval of 1 unit. The graph is 2 pi periodic with asymptotes at x equals plus or minus n pi. It touches the lines y equals negative 1 point 8 at (0 comma negative 1 point 8) and y equals negative 2 point 2 at (pi comma negative 2 point 2) and (negative pi comma negative 2 point 2).

Which function will have a y-intercept at –1 and an amplitude of 2?

f (x) = negative sine (X) minus 1

f (x) = negative 2 sine (x) minus 1

f (x) = negative cosine (x)

f (x) = negative 2 cosine (x) minus 1

What is the maximum of f(x) = sin(x)?

Negative 2 pi

–1

2 pi

What function is graphed below?

y equal to cotangent (x minus StartFraction pi over 4 EndFraction)

y equal to tangent (x minus StartFraction pi over 4 EndFraction)

y equal to cotangent (x plus StartFraction pi over 4 EndFraction)

y equal to tangent (x plus StartFraction pi over 4 EndFraction)

Which function describes the graph below?

y = 8 cosine (x) + 3

y = 4 cosine (x) + 3

y = 4 sine (x) + 3

y = 8 sine (x) + 3

Mark sits on a swing that is 2.5 feet off the ground. Swinging as hard as he can, the swing reaches a height of 6 feet. Assuming Mark holds a steady pace, the height of the swing could be represented by a cosine curve.If Mark makes a full swing forward and backward in 3 seconds, which graph below could represent the height of the swing, in feet, for any time, t?

On a coordinate plane, seconds is on the x-axis and feet is on the y-axis. A curve starts at (0, 3). It has a maximum of y = 6 and a minimum of y = 3. It goes through 1 cycle in 1.5 seconds.

On a coordinate plane, seconds is on the x-axis and feet is on the y-axis. A curve starts at (0, 3). It has a maximum of y = 8 and a minimum of y = 4. It goes through 1 cycle in 1.5 seconds.

On a coordinate plane, seconds is on the x-axis and feet is on the y-axis. A curve starts at (0, 3). It has a maximum of y = 6 and a minimum of y = 3. It goes through 1 cycle in 3 seconds.

On a coordinate plane, seconds is on the x-axis and feet is on the y-axis. A curve starts at (0, negative 2). It has a maximum of y = 2 and a minimum of y = negative 2. It goes through 1 cycle in 1.5 seconds.

Which of the following could be the equation of the function below?

y = negative 2 cosine (4 (x + pi)) minus 1

y = 2 cosine (x + pi) + 1

y = negative 2 cosine (2 (x + pi)) minus 1

y = 2 cosine (4 (x + pi)) + 2

Did you find these answers helpful?

Absolute Value Functions Answers

More from this Course

TRY EDGENUITY HACKS