Determine the amplitude, period, and phase shift for the given function. - cos(2x - 5) y=1- 1 amplitude period phase shift Graph the function over one period. y 3.0 2.5 2.0 1.5 1.0 0.5 y -0.5 -1.0 -1.5 O-2.0 2л 3 3 7x 6 7x X X y 1.0 0- 0.5 -0.5 A 2A y 2.0 1.5 1.0 0.5 76 | 25/0 2A 3 7x 6 X X

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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There is a sceond part to this because I wasn't able to get it all in one.

**Determine the amplitude, period, and phase shift for the given function.**

\[ y = 1 - \cos\left(2x - \frac{\pi}{3}\right) \]

- **Amplitude:** [   ]
- **Period:** [   ]
- **Phase Shift:** [   ]

**Graph the function over one period.**

Below are four graph options for the function \( y = 1 - \cos\left(2x - \frac{\pi}{3}\right) \). Each graph displays it over one period. Examine their characteristics to determine the correct graph corresponding to the given function.

1. **Top Left Graph:** 
    - Vertical range from approximately 0.5 to 3.0.
    - Completes one cycle within the interval marked from \( \frac{\pi}{6} \) to \( \frac{7\pi}{6} \).

2. **Top Right Graph:** 
    - Vertical range from approximately -1.0 to 1.0.
    - Completes one cycle within the interval marked from \( \frac{\pi}{6} \) to \( \frac{7\pi}{6} \).

3. **Bottom Left Graph:**
    - Vertical range from approximately -2.0 to 0.0.
    - Completes one cycle within the interval marked from \( \frac{\pi}{6} \) to \( \frac{7\pi}{6} \).

4. **Bottom Right Graph:**
    - Vertical range from approximately 0.0 to 2.0.
    - Completes one cycle within the interval marked from \( \frac{\pi}{6} \) to \( \frac{7\pi}{6} \).

Select the graph that accurately represents the complete cycle and characteristics of the function \( y = 1 - \cos\left(2x - \frac{\pi}{3}\right) \).
Transcribed Image Text:**Determine the amplitude, period, and phase shift for the given function.** \[ y = 1 - \cos\left(2x - \frac{\pi}{3}\right) \] - **Amplitude:** [ ] - **Period:** [ ] - **Phase Shift:** [ ] **Graph the function over one period.** Below are four graph options for the function \( y = 1 - \cos\left(2x - \frac{\pi}{3}\right) \). Each graph displays it over one period. Examine their characteristics to determine the correct graph corresponding to the given function. 1. **Top Left Graph:** - Vertical range from approximately 0.5 to 3.0. - Completes one cycle within the interval marked from \( \frac{\pi}{6} \) to \( \frac{7\pi}{6} \). 2. **Top Right Graph:** - Vertical range from approximately -1.0 to 1.0. - Completes one cycle within the interval marked from \( \frac{\pi}{6} \) to \( \frac{7\pi}{6} \). 3. **Bottom Left Graph:** - Vertical range from approximately -2.0 to 0.0. - Completes one cycle within the interval marked from \( \frac{\pi}{6} \) to \( \frac{7\pi}{6} \). 4. **Bottom Right Graph:** - Vertical range from approximately 0.0 to 2.0. - Completes one cycle within the interval marked from \( \frac{\pi}{6} \) to \( \frac{7\pi}{6} \). Select the graph that accurately represents the complete cycle and characteristics of the function \( y = 1 - \cos\left(2x - \frac{\pi}{3}\right) \).
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