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

Performance Task: Modeling with Sinusoidal Functions — Unit test Answers

25 verified answers
1
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Which functions are symmetric with respect to the origin?

A
y = arcsinx and y = arccosx
B
y = arccosx and y = arctanx
C
y = arctanx and y = arccotx
D
y = arcsinx and y = arctanx
2
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In which quadrant(s) is csc(x) positive?

A
quadrant I only
B
quadrant II only
C
quadrants I and II
D
quadrants I and III
3

Which expression is equivalent to 30°?

A
Inverse of cosine (StartFraction StartRoot 3 EndRoot Over 2 EndFraction)
Option A
B
Inverse of sine (StartFraction StartRoot 3 EndRoot Over 2 EndFraction)
Option B
C
Sine (StartFraction StartRoot 3 EndRoot Over 2 EndFraction)
Option C
D
Cosine (StartFraction StartRoot 3 EndRoot Over 2 EndFraction)
Option D
4

How many degrees is radians?

Question illustration
A
84.375°
B
93.75°
C
168.75°
D
337.5°
5

Which is an x-intercept of the graph of the function ?

Question illustration
A
(minus StartFraction 2pi over 3 EndFraction , 0)
Option A
B
(minus StartFraction pi over 3 EndFraction , 0)
Option B
C
(StartFraction pi over 6 EndFraction , 0)
Option C
D
(StartFraction 5pi over 6 EndFraction , 0)
Option D
6

At a certain location, the number of hours of sunlight is modeled by y = where x represents the number of weeks after the summer solstice.Based on the model, what is the minimum number of hours of sunlight at this location?

Question illustration
A
3.2
B
5.6
C
6.4
D
13.0
7

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

Question illustration
A
y equal to 2 cosecant left-square-bracket 0 point 5 (x plus StartFraction pi over 2 EndFraction) right-square-bracket minus 1.
Option A
B
y equal to 2 cosecant left-square-bracket 2 (x plus StartFraction pi over 4 EndFraction) minus 1 right-square-bracket.
Option B
C
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.
Option C
D
y equal to 0 point 5 cosecant left-square-bracket 2 (x plus StartFraction pi over 4 EndFraction) right-square-bracket minus 1.
Option D
8

Suppose you want to transform the graph of the function into the graph of the function . Which transformations should you perform?

Question illustration
A
Reflect the graph of the first function across the x-axis, translate it units to the left, and translate it 2 units up.
Option A
B
Reflect the graph of the first function across the x-axis, translate it units to the right, and translate it 2 units up.
Option B
C
Reflect the graph of the first function across the line , translate it units to the left, and translate it 2 units up.
Option C
D
Reflect the graph of the first function across the line , translate it units to the right, and translate it 2 units up.
Option D
9

Which of the following is the graph of ?

Question illustration
A
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).
Option A
B
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).
Option B
C
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).
Option C
D
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).
Option D
10

Suppose the function h(x) = sinx is translated units left and 11 units down. Which graph represents the result?

Question illustration
A
On a coordinate plane, a function has a maximum of negative 10 and minimum of negative 12. It completes one period at 2 pi. It decreases through the y-axis at (0, negative 11).
Option A
B
On a coordinate plane, a function has a maximum of negative 10 and minimum of negative 12. It completes one period at 2 pi. It crosses the y-axis at (0, negative 10).
Option B
C
On a coordinate plane, a function has a maximum of negative 10 and minimum of negative 12. It completes one period at 2 pi. It increases through the y-axis at (0, negative 11).
Option C
D
On a coordinate plane, a function has a maximum of negative 10 and minimum of negative 12. It completes one period at 2 pi. It crosses the y-axis at (0, negative 12).
Option D
11

What is the equation of the graph below?

Question illustration
A
y = sec(x) + 2
B
y = csc(x) + 2
C
y = csc(x + 2)
D
y = sec(x + 2)
12

The table shows the temperatures in degrees Celsius, y, inside a shed at x hours past noon. The maximum and minimum temperatures are shown.

Question illustration
A
y = 3 cosine (StartFraction pi Over 12 EndFraction x minus StartFraction pi Over 3 EndFraction) + 17
Option A
B
y = 3 cosine (StartFraction pi Over 12 EndFraction x minus StartFraction pi Over 4 EndFraction) + 17
Option B
C
y = 6 cosine (StartFraction pi Over 12 EndFraction x minus StartFraction pi Over 3 EndFraction) + 17
Option C
D
y = 6 cosine (StartFraction pi Over 12 EndFraction x minus StartFraction pi Over 4 EndFraction) + 17
Option D
13

How does the graph of y = sec(x + 3) – 7 compare with the graph of y = sec(x)?

A
It is the graph of y = sec(x) shifted 3 units right and 7 units up.
B
It is the graph of y = sec(x) shifted 3 units left and 7 units up.
C
It is the graph of y = sec(x) shifted 3 units left and 7 units down.
D
It is the graph of y = sec(x) shifted 3 units right and 7 units down.
14

The function g(x) represents f(x) = after translating units left and 4 units up.Which equation represents g(x)?

Question illustration
A
g (x) = 9 cosine (x minus StartFraction pi Over 3 EndFraction) minus 1
Option A
B
g (x) = 9 cosine (x minus StartFraction pi Over 3 EndFraction) + 7
Option B
C
g (x) = 9 cosine (x minus StartFraction 2 pi Over 3 EndFraction) minus 1
Option C
D
g (x) = 9 cosine (x minus StartFraction 2 pi Over 3 EndFraction) + 7
Option D
15

Suppose tan(b) = –2, and the terminal side of b is located in quadrant II. What is cot(b)?

A
–2
B
Negative one-half
Option B
C
One-half
Option C
D
2
16

A seat on a Ferris wheel is level with the center of the wheel. The diameter of the wheel is 200 feet. Suppose the wheel rotates 60°, causing the height of the seat to decrease. How much closer to the ground is the seat after the rotation?

A
50 feet
B
feet
Option B
C
100 feet
D
feet
Option D
17

Let a function y represent the water level in a harbor measured in meters, and let x represent the number of hours since high tide. At time x = 0, the water level is 19.5 meters (a maximum). At time x = 6.26 hours, the water level is 10.5 meters (a minimum). The period of the function is 12.5 hours.After how many hours is the water expected to reach a depth of 17 meters for the first time? Round to the nearest tenth of an hour.

A
2.2 hours
B
6.3 hours
C
12.1 hours
D
12.5 hours
18

Review the graph.

Question illustration
A
y = tanx
B
y = cosx
C
y = tan-1x
D
y = cos-1x
19

Which transformation should be applied to the graph of the function to obtain the graph of the function ?

Question illustration
A
a vertical stretch, a horizontal compression to make the period , a horizontal shift of units to the right, and a vertical shift of 4 units up
Option A
B
a vertical stretch, a horizontal compression to make the period , a horizontal shift of units to the right, and a vertical shift of 4 units up
Option B
C
a vertical stretch, a horizontal compression to make the period , a horizontal shift of units to the right, and a vertical shift of 4 units up
Option C
D
a vertical stretch, a horizontal compression to make the period , a horizontal shift of units to the right, and a vertical shift of 4 units up
Option D
20

What is the period of the function ?

Question illustration
A
units
Option A
B
units
Option B
C
units
Option C
D
units
Option D

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