Consider the function f(x) = 4 sin (5 (x – 2))+6. State the amplitude A, period P, and midline. State the phase shift and vertical translation. In the full period [0, P], state the maximum and minimum y-values and their corresponding x-values. Enter the exact answers. Amplitude: A = Number Period: P =
Consider the function f(x) = 4 sin (5 (x – 2))+6. State the amplitude A, period P, and midline. State the phase shift and vertical translation. In the full period [0, P], state the maximum and minimum y-values and their corresponding x-values. Enter the exact answers. Amplitude: A = Number Period: P =
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![a
Va
|a|
sin (a)
x =
a
ab
Va
|a|
sin (a)
y =
For x in the interval [0, P], the minimum y-value and corresponding x-value is at:
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sin (a)
x =
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Va
Ja
sin (a)
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Transcribed Image Text:a
Va
|a|
sin (a)
x =
a
ab
Va
|a|
sin (a)
y =
For x in the interval [0, P], the minimum y-value and corresponding x-value is at:
a
ab
Va
Ja
sin (a)
x =
a
Va
Ja
sin (a)
y =
![Consider the function f (x) = 4 sin (5
(x – 2)) + 6. State the amplitude A, period P, and
midline. State the phase shift and vertical translation. In the full period [0, P], state the maximum and
minimum y-values and their corresponding x-values.
Enter the exact answers.
Amplitude: A =
Number
Period: P =
Va
la|
sin (a)
Midline: y =
Number
The phase shift is
Click for List
The vertical translation is
Click for List
Hints for the maximum and minimum values of f (x):
• The maximum value of y = sin (x) is y =1 and the corresponding x values are x =
and
multiples of 2 T less than and more than this x value. You may want to solve 5 (x – 2)
• The minimum value of y = sin (x) is y = -1 and the corresponding a values are æ =
and
2
multiples of 2 r less than and more than this x value. You may want to solve 4 (x – 2)
3 п
• If you get a value for æ that is less than 0, you could add multiples of P to get into the next cycles.
• If you get a value for x that is more than P, you could subtract multiples of P to get into the
previous cycles.
For x in the interval [0, P], the maximum y-value and corresponding x-value is at:](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc1a9c439-91af-4d96-a160-0e220e82a4ad%2F1243d56e-b0a5-4e9d-b16f-2b78c29cff87%2Fw4umred_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the function f (x) = 4 sin (5
(x – 2)) + 6. State the amplitude A, period P, and
midline. State the phase shift and vertical translation. In the full period [0, P], state the maximum and
minimum y-values and their corresponding x-values.
Enter the exact answers.
Amplitude: A =
Number
Period: P =
Va
la|
sin (a)
Midline: y =
Number
The phase shift is
Click for List
The vertical translation is
Click for List
Hints for the maximum and minimum values of f (x):
• The maximum value of y = sin (x) is y =1 and the corresponding x values are x =
and
multiples of 2 T less than and more than this x value. You may want to solve 5 (x – 2)
• The minimum value of y = sin (x) is y = -1 and the corresponding a values are æ =
and
2
multiples of 2 r less than and more than this x value. You may want to solve 4 (x – 2)
3 п
• If you get a value for æ that is less than 0, you could add multiples of P to get into the next cycles.
• If you get a value for x that is more than P, you could subtract multiples of P to get into the
previous cycles.
For x in the interval [0, P], the maximum y-value and corresponding x-value is at:
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