Consider the function f(2)=2 sin ((z-3)) +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 z-values. Enter the exact answers. Amplitude: A-2 Period: P Midline: y The phase shift is The vertical translation is
Consider the function f(2)=2 sin ((z-3)) +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 z-values. Enter the exact answers. Amplitude: A-2 Period: P Midline: y The phase shift is The vertical translation is
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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![Consider the function \( f(x) = 2 \sin \left( \frac{\pi}{4} (x - 3) \right) + 6 \). 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:** \( A = \)
\[ \boxed{2} \]
**Period:** \( P = \)
\[ \boxed{8} \]
**Midline:** \( y = \)
\[ \boxed{6} \]
**The phase shift is:**
\[ \boxed{\text{3 units to the right}} \]
**The vertical translation is:**
\[ \boxed{\text{6 units up}} \]
### 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 \( x = \frac{\pi}{4} + 2k\pi \) and multiples of \( 2 \pi \) less than and more than this \( x \) value. You may want to solve \(\frac{\pi}{4} (x - 3) = \frac{\pi}{2}\).
- The minimum value of \( y = \sin (x) \) is \( y = -1 \) and the corresponding \( x \) values are \( x = 3 \frac{\pi}{4} + 2k\pi \) and multiples of \( 2 \pi \) less than and more than this \( x \) value. You may want to solve \(\frac{\pi}{4} (x - 3) = 3 \frac{\pi}{4}\).
- If you get a value for \( x \) 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%2F2da59d05-ea7a-47ad-8289-54dec09680e5%2F132d7132-44a8-465c-935f-39ba42323b89%2Fxg9yo6s_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider the function \( f(x) = 2 \sin \left( \frac{\pi}{4} (x - 3) \right) + 6 \). 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:** \( A = \)
\[ \boxed{2} \]
**Period:** \( P = \)
\[ \boxed{8} \]
**Midline:** \( y = \)
\[ \boxed{6} \]
**The phase shift is:**
\[ \boxed{\text{3 units to the right}} \]
**The vertical translation is:**
\[ \boxed{\text{6 units up}} \]
### 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 \( x = \frac{\pi}{4} + 2k\pi \) and multiples of \( 2 \pi \) less than and more than this \( x \) value. You may want to solve \(\frac{\pi}{4} (x - 3) = \frac{\pi}{2}\).
- The minimum value of \( y = \sin (x) \) is \( y = -1 \) and the corresponding \( x \) values are \( x = 3 \frac{\pi}{4} + 2k\pi \) and multiples of \( 2 \pi \) less than and more than this \( x \) value. You may want to solve \(\frac{\pi}{4} (x - 3) = 3 \frac{\pi}{4}\).
- If you get a value for \( x \) 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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I am stuck on the maximum and minimum values of y and corresponding x. Will you please assist on that. It is the last part of the question in the picture.
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