AnswersS1S-OC Pre-Calculus A E3700 - AGPerformance Task: Modeling with Sinusoidal Functions

Performance Task: Modeling with Sinusoidal Functions — Unit test Answers

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Which graph represents the function y = cos(4x)?

A
On a coordinate plane, a function has a maximum at 1 and minimum at negative 1. It completes one period at pi. It crosses the y-axis at (0, 1).
Option A
B
On a coordinate plane, a function has a maximum at 1 and minimum at negative 1. It completes one period at StartFraction pi Over 2 EndFraction. It crosses the y-axis at (0, 1).
Option B
C
On a coordinate plane, a function has a maximum at 1 and minimum at negative 1. It completes one period at pi. It crosses the y-axis at (0, 0).
Option C
D
On a coordinate plane, a function has a maximum at 1 and minimum at negative 1. It completes one period at StartFraction pi Over 2 EndFraction. It crosses the y-axis at (0, 0).
Option D
2
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On which interval are both the sine and cosine functions increasing?

A
(StartFraction 3 pi Over 2 EndFraction, 2 pi)
Option A
B
(StartFraction pi Over 2 EndFraction, pi)
Option B
C
(0, pi)
Option C
D
(pi, StartFraction 3 pi Over 2 EndFraction
Option D
3

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

Question illustration
A
StartFraction 5 Over StartRoot 89 EndRoot EndFraction
Option A
B
StartFraction 8 Over StartRoot 89 EndRoot EndFraction
Option B
C
StartFraction StartRoot 89 EndRoot Over 8 EndFraction
Option C
D
StartFraction StartRoot 89 EndRoot Over 5 EndFraction
Option D
4

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.

Question illustration
A
the length of the pipe
B
the distance between the tower and the farmhouse
C
the time it takes for the pipe to complete one full circle
D
the difference between the maximum and minimum distances from the tip of the pipe to the farmhouse
5

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?

Question illustration
A
August
B
September
C
November
D
December
6

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

A
Restrict the range to (negative StartFraction pi Over 2 EndFraction, StartFraction pi Over 2 EndFraction)
Option A
B
Restrict the range to left-bracket negative StartFraction pi Over 2 EndFraction, StartFraction pi Over 2 EndFraction right-bracket
Option B
C
Restrict the domain to (negative StartFraction pi Over 2 EndFraction, StartFraction pi Over 2 EndFraction)
Option C
D
Restrict the domain to left-bracket negative StartFraction pi Over 2 EndFraction, StartFraction pi Over 2 EndFraction right-bracket
Option D
7

Which graph represents ?

Question illustration
A
On a coordinate plane, a function has a maximum of 6 and minimum of 4. It completes one period at pi. It crosses the y-axis at (0, 4).
Option A
B
On a coordinate plane, a function has a maximum of 6 and minimum of 4. It completes one period at pi. It decreases through the y-axis at (0, 5).
Option B
C
On a coordinate plane, a function has a maximum of 7 and minimum of 3. It completes one period at 2 pi. It crosses the y-axis at (0, 3).
Option C
D
On a coordinate plane, a function has a maximum of 7 and minimum of 3. It completes one period at 2 pi. It decreases through the y-axis at (0, 5).
Option D
8

Review the graph.

Question illustration
A
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.
Option A
B
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.
Option B
C
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.
Option C
D
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.
Option D
9

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)?

Question illustration
A
the amplitude
B
the frequency
C
the phase shift
D
the vertical shift
10

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

A
–1
B
0
C
1
D
StartFraction pi Over 2 EndFraction
Option D
11

Which is equal to –214°?

A
radians
Option A
B
radians
Option B
C
radians
Option C
D
radians
Option D
12

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?

A
radians
Option A
B
radians
Option B
C
radians
Option C
D
radians
Option D
13

Review the graph of y = sin(x).

Question illustration
A
domain: [0, 2π]; range: [–1, 1]
B
domain: [–1, 1]; range: [0, 2π]
C
domain: [–1, 1]; range: (–ꝏ, ꝏ)
D
domain: (–ꝏ, ꝏ); range: [–1, 1]
14

It takes 1.5 seconds for a grandfather clock's pendulum to swing from left (initial position) to right, covering a horizontal distance of 10 inches.Which function models the horizontal displacement as a function of time in seconds?

A
y = 5 cosine (StartFraction 2 pi Over 3 EndFraction x)
Option A
B
y = 5 cosine (StartFraction 4 pi Over 3 EndFraction x)
Option B
C
y = 10 cosine (StartFraction 2 pi Over 3 EndFraction x)
Option C
D
y = 10 cosine (StartFraction 4 pi Over 3 EndFraction x)
Option D
15

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?

A
y = 0.5 sine (180 pi x) + 13
Option A
B
y = 12.5 sine (180 pi x) + 13
Option B
C
y = 0.5 sine (180 pi x minus StartFraction pi Over 2 EndFraction) + 13
Option C
D
y = 12.5 sine (180 pi x minus StartFraction pi over 2 EndFraction) + 13
Option D

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