Answers S1S-OC Pre-Calculus A E3700 - AGPerformance Task: Modeling with Sinusoidal Functions

Performance Task: Modeling with Sinusoidal Functions — Unit test Answers

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Consider the graphs of j(x) = and k(x) = .Which feature of the graph of k(x) is different from the graph of j(x)?

the amplitude

the frequency

the phase shift

the vertical shift

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Let cot(x) = , with 0 < x < 90°. What is sin(x)?

StartFraction 5 Over StartRoot 89 EndRoot EndFraction

StartFraction 8 Over StartRoot 89 EndRoot EndFraction

StartFraction StartRoot 89 EndRoot Over 8 EndFraction

StartFraction StartRoot 89 EndRoot Over 5 EndFraction

What is the value of cos(tan-1(0))?

–1

StartFraction pi Over 2 EndFraction

On which interval are both the sine and cosine functions increasing?

(StartFraction 3 pi Over 2 EndFraction, 2 pi)

(StartFraction pi Over 2 EndFraction, pi)

(0, pi)

(pi, StartFraction 3 pi Over 2 EndFraction

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

y equal to 2 secant (x plus StartFraction pi over 6 EndFraction) plus 2.

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

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

y equal to 2 secant (x plus 2) plus StartFraction pi over 6 EndFraction.

The parent cosecant function is shifted 2 units down, and its period is changed to . Which of the following is the graph of the transformed function?

On a coordinate plane, the x axis ranges from negative 6 pi to 6 pi with an interval of pi units and the y axis ranges from negative 6 to 2 with an interval of 2 units. A graph of a function with asymptotes at x equals plus or minus n pi is drawn. It touches the line y equals negative 1 at (3 by 2 pi comma negative 1) and (negative 9 by 2 pi comma negative 1). Another line y equals negative 3 touches at (3 by 2 pi comma negative 3) and (negative 9 by 2 pi comma negative 3).

On a coordinate plane, the x axis ranges from negative 6 pi to 6 pi with an interval of pi units and the y axis ranges from negative 4 to 4 with an interval of 2 units. A graph of a function with asymptotes at x equals plus or minus n pi is drawn. It touches the line y equals 1 at (3 by 2 pi comma1) and (negative 9 by 2 pi comma 1). Another line y equals negative 1 touches at (9 by 2 pi comma negative 1) and (negative 3 by 2 pi comma negative 1).

On a coordinate plane, the x axis ranges from negative 6 pi to 6 pi with an interval of pi units and the y axis ranges from negative 6 to 2 with an interval of 2 units. A graph of a function with asymptotes at x equals plus or minus n pi is drawn. It touches the line y equals 1 at (6 pi comma1), (0 comma 1) and (negative 6 pi comma 1). Another line y equals negative 3 touches at (3 pi comma negative 3) and (negative 3 pi comma negative 3).

On a coordinate plane, the x axis ranges from negative 6 pi to 6 pi with an interval of pi units and the y axis ranges from negative 4 to 4 with an interval of 2 units. A graph of a function with asymptotes at x equals plus or minus n pi is drawn. It touches the line y equals 1 at (6 pi comma1), (0 comma 1) and (negative 6 pi comma 1). Another line y equals negative 2 touches at (3 pi comma negative 1) and (negative 3 pi comma negative 1).

What restriction should be applied to y = tanx for y = arctanx to be defined?

Restrict the range to (negative StartFraction pi Over 2 EndFraction, StartFraction pi Over 2 EndFraction)

Restrict the range to left-bracket negative StartFraction pi Over 2 EndFraction, StartFraction pi Over 2 EndFraction right-bracket

Restrict the domain to (negative StartFraction pi Over 2 EndFraction, StartFraction pi Over 2 EndFraction)

Restrict the domain to left-bracket negative StartFraction pi Over 2 EndFraction, StartFraction pi Over 2 EndFraction right-bracket

A waterwheel has a radius of 5 feet. The center of the wheel is 2 feet above the waterline. You notice a white mark at the top of the wheel. How many radians would the wheel have to rotate for the white mark to be 3 feet below the waterline?

radians

A circular crop field has an irrigation system in which a pipe, with one end attached to a tower at the center of the field, turns continuously to deliver water. The horizontal distance, in meters, from the tip of the pipe to the farmhouse is represented by y = , where x represents time in hours.

the length of the pipe

the distance between the tower and the farmhouse

the time it takes for the pipe to complete one full circle

the difference between the maximum and minimum distances from the tip of the pipe to the farmhouse

What is the amplitude of the cosine function corresponding to the secant function graphed below?

–2

–1

Which is equal to –214°?

radians

Annabelle’s bicycle has a wheel radius of 13 inches. She places a sticker on the wheel so that its minimum height above the ground is 0.5 inches. When she rides her bicycle, the wheel completes 90 revolutions every minute. The sticker begins at its minimum height above the ground.Which equation models the height in inches of the sticker after x minutes?

y = 0.5 sine (180 pi x) + 13

y = 12.5 sine (180 pi x) + 13

y = 0.5 sine (180 pi x minus StartFraction pi Over 2 EndFraction) + 13

y = 12.5 sine (180 pi x minus StartFraction pi over 2 EndFraction) + 13

The average high temperature during the hottest month in Beijing, China, is 72°F. The average high temperature during the coldest month in Beijing is 18°F. The function , where m represents the number of months after January, models the temperature throughout the year in Beijing.During which month in the year would the temperature reach 55°F?

August

September

November

December

Judy knows that the function graphed below is a transformation of the parent function . Since the period and asymptotes are the same as those of the parent function, she knows that there were no horizontal stretches, compressions, or translations. She can also tell that there were no reflections since the general shape of the graph is the same as that of the parent function. Which statement is correct regarding the transformations that were applied?

Since the y-intercept of the graph is , the graph of the parent function was translated 0.5 units down, and since the graph passes through the point instead of , the graph was vertically compressed.

Since the y-intercept of the graph is , the graph of the parent function was translated 0.5 units down, and since the graph passes through the point instead of , the graph was vertically stretched.

Since the y-intercept of the graph is , the graph of the parent function was translated 1.5 units down, and since the graph passes through the point instead of , the graph was vertically compressed.

Since the y-intercept of the graph is , the graph of the parent function was translated 1.5 units down, and since the graph passes through the point instead of , the graph was vertically stretched.

Review the graph.

On a coordinate plane, a function approaches y = negative StartFraction pi Over 2 EndFraction in quadrant 3, increases through an inflection point at (0, 0), and approaches y = StartFraction pi over 2 EndFraction in quadrant 1.

On a coordinate plane, a function approaches x = negative StartFraction pi Over 2 EndFraction in quadrant 2, has an inflection point at (0, 0), and approaches x = StartFraction pi Over 2 EndFraction in quadrant 4.

On a coordinate plane, a function approaches y = negative StartFraction pi Over 2 EndFraction in quadrant 4, increases through an inflection point at (0, 0), and approaches y = StartFraction pi over 2 EndFraction in quadrant 2.

On a coordinate plane, a function approaches x = negative StartFraction pi Over 2 EndFraction in quadrant 3, has an inflection point at (0, 0), and approaches x = StartFraction pi Over 2 EndFraction in quadrant 1.

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Performance Task: Modeling with Sinusoidal Functions — Unit test Answers

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