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MHF4U k1+, Advanced Functions, 12, University Virtual High School
Unit Assignment: Trigonometry unit and graph assignment
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Question 1
For each of the following functions, state
the domain;
the range
the minimum and maximum values
the period
the phase shift
and the amplitude
a. 𝑓 𝑥 = 4 sin
1
3
𝑥 + 2𝜋 −
3
2
A) given,
𝑓 𝑥 = 4 sin ((1/3) x + 2π) −
3
2
Domain {x|x E R}
Range -4 <4*sin
1
3
x + 2π < 4
-4 ≤4 sin
1
3
x + 2π < 4
Now subtract (3/2) on both sides
−4 – (3/2) ≤ 4 sin ((1/3) x + 2π) – (3/2) ≤ 4 −
3
2
−
11
2
≤ 4sin
1
3
x + 2π –
3
2
≤
5
2
Range f x −
11
2
≤ f x ≤
5
2
, f(x) E R}
Minimum value = -11/2
Maximum value= 5/2
Phase Shift = 6 π (left)
Amplitude = 4
Period= 2π/ (1/3)
= 2π / (1/3)
= 6π
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Question 2
Describe the transformations in each graph.
Sketch the graphs of the following functions by
hand, using transformations. Show your work
(show how the transformations map from the
base function to the transformed function) for
the graph in addition to listing the information.
Graph values from 0 ≤ x ≤ 2π.
a. f(x) = −2 cos 3𝑥 −
𝜋
3
+
1
2
b. f(x) =
1
4
𝑠𝑖𝑛
1
2
𝑥 + 𝜋 − 3
Answer 2
a) Phase Shift = π/9 (right)
Period = 2π/3
Amplitude = 2
Vertical Shift = ½
b) Phase Shift = 2π (left)
Period = 2π/ (1/2) = 4π
Amplitude = 1/4
Vertical Shift = -3
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Question 3
For each of the graphs below, create a function
of the form f(x) = a cos(k(x − d)) + c or f(x) = a
sin(k(x − d)) + c. Show all of your calculations
a.
b.
Please contact to get complete assignment - admin@panhelp.com
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Question 4
On a particular lake, the difference between high
and low tide is 6 hours. At low tide, 6 a.m., a
student measures a 1.4 m distance from the
dock she is standing on, down to the water. two
hours later, she measures the distance from the
dock down to the water to be 1.29 m. After three
hours, the distance is 1.175 m down to the
water.
a. Determine the function for the distance from
the dock down to the water with respect to
the number of hours since midnight.
b. Determine the distance to the water at 4:30
a.m. and 1:45 p.m.
Please contact to get complete assignment - admin@panhelp.com

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Trigonometric Functions and Graphs Assignment-Advance Function - VHS - MHF4U

  • 1. PanHelp MHF4U k1+, Advanced Functions, 12, University Virtual High School Unit Assignment: Trigonometry unit and graph assignment Assignment Help | 100% Plagiarism Free | Success Assured | Email Now to get quote – admin@panhelp.com
  • 2. Assignment Help | 100% Plagiarism Free | Success Assured | Email Now to get quote – admin@panhelp.com Question 1 For each of the following functions, state the domain; the range the minimum and maximum values the period the phase shift and the amplitude a. 𝑓 𝑥 = 4 sin 1 3 𝑥 + 2𝜋 − 3 2 A) given, 𝑓 𝑥 = 4 sin ((1/3) x + 2π) − 3 2 Domain {x|x E R} Range -4 <4*sin 1 3 x + 2π < 4 -4 ≤4 sin 1 3 x + 2π < 4 Now subtract (3/2) on both sides −4 – (3/2) ≤ 4 sin ((1/3) x + 2π) – (3/2) ≤ 4 − 3 2 − 11 2 ≤ 4sin 1 3 x + 2π – 3 2 ≤ 5 2 Range f x − 11 2 ≤ f x ≤ 5 2 , f(x) E R} Minimum value = -11/2 Maximum value= 5/2 Phase Shift = 6 π (left) Amplitude = 4 Period= 2π/ (1/3) = 2π / (1/3) = 6π
  • 3. Assignment Help | 100% Plagiarism Free | Success Assured | Email Now to get quote – admin@panhelp.com Question 2 Describe the transformations in each graph. Sketch the graphs of the following functions by hand, using transformations. Show your work (show how the transformations map from the base function to the transformed function) for the graph in addition to listing the information. Graph values from 0 ≤ x ≤ 2π. a. f(x) = −2 cos 3𝑥 − 𝜋 3 + 1 2 b. f(x) = 1 4 𝑠𝑖𝑛 1 2 𝑥 + 𝜋 − 3 Answer 2 a) Phase Shift = π/9 (right) Period = 2π/3 Amplitude = 2 Vertical Shift = ½ b) Phase Shift = 2π (left) Period = 2π/ (1/2) = 4π Amplitude = 1/4 Vertical Shift = -3
  • 4. Assignment Help | 100% Plagiarism Free | Success Assured | Email Now to get quote – admin@panhelp.com Question 3 For each of the graphs below, create a function of the form f(x) = a cos(k(x − d)) + c or f(x) = a sin(k(x − d)) + c. Show all of your calculations a. b. Please contact to get complete assignment - admin@panhelp.com
  • 5. Assignment Help | 100% Plagiarism Free | Success Assured | Email Now to get quote – admin@panhelp.com Question 4 On a particular lake, the difference between high and low tide is 6 hours. At low tide, 6 a.m., a student measures a 1.4 m distance from the dock she is standing on, down to the water. two hours later, she measures the distance from the dock down to the water to be 1.29 m. After three hours, the distance is 1.175 m down to the water. a. Determine the function for the distance from the dock down to the water with respect to the number of hours since midnight. b. Determine the distance to the water at 4:30 a.m. and 1:45 p.m. Please contact to get complete assignment - admin@panhelp.com