Math | Graded Assignment Answer Key | Unit Test, Part 2 | Graphs of Sinusoidal Functions
Graded Assignment Answer Key
Unit Test, Part 2: Graphs of Sinusoidal Functions
Use or adapt the feedback in this Answer Key as you grade each student paper. Answers will vary. Therefore,
you must examine each answer based upon its own merits. Representative examples are shown here.
Total Score: 15 points
1. Graph the function
f ( x)  sin  x  – 2 .
Model Answer
Award points for specific answers as shown (for a total of 0–5 points).
Points
Concept Addressed
Feedback for Students Who Struggled with
Concept
5
Correctly graphs the function
 3
Determine the values of f(x) for x  0, , , ,
2
2
and 2 . Plot these points to help draw the
graph.
2.
f ( x)  sin  x  – 2 .
Graph the function f ( x )  cos(2x )  1 .
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Math | Graded Assignment Answer Key | Unit Test, Part 2 | Graphs of Sinusoidal Functions
Model Answer
Award points for specific answers as shown (for a total of 0–5 points).
Points
Concept Addressed
Feedback for Students Who Struggled with
Concept
5
Correctly graph the function
f ( x )  cos(2x )  1 .
 3
Determine the values of f(x) for x  0, , , ,
2
2
and 2 . Plot these points to help draw the
graph.
3. A scientist recorded the movement of a pendulum for 10 s. The scientist began recording when the pendulum
was at its resting position. The pendulum then moved right (positive displacement) and left (negative
displacement) several times. The pendulum took 4 s to swing to the right and the left and then return to its
resting position. The pendulum’s furthest distance to either side was 6 in. Graph the function that represents
the pendulum’s displacement as a function of time.
(a) Write an equation to represent the displacement of the pendulum as a function of time.
(b) Graph the function.
Model Answer
(a) Identify the features of the graph.
The function has a value of 0 when t = 0, so the graph is a sine function.
The amplitude is 6 and the period is
2  
.
4
2
An equation for the function is f (t )  6 sin  t  .
2
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Math | Graded Assignment Answer Key | Unit Test, Part 2 | Graphs of Sinusoidal Functions
(b)
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Copying or distributing without K12’s written consent is prohibited.
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Math | Graded Assignment Answer Key | Unit Test, Part 2 | Graphs of Sinusoidal Functions
Award points for specific answers as shown (for a total of 0–5 points).
Points
Concept Addressed
Feedback for Students Who Struggled with
Concept
3
Writes an equation for the function.
Read the problem statement. Look for
information that describes the amplitude and
period of the function.
2
Graphs the function.
Evaluate the function for x = 0, 1, 2, 3, and 4.
Plot these values on the coordinate plane to help
draw the graph.
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Copying or distributing without K12’s written consent is prohibited.
Page 4 of 4