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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![### Graph Analysis and Possible Equations
**Task**: Write a possible equation for the graphs below:
#### a)
**Detailed Description**:
- **Type of Graph**: This appears to be a sinusoidal graph, specifically a cosine graph.
- **Amplitude**: The maximum value is 2 and the minimum value is -2, suggesting that the amplitude is 2.
- **Period**: The graph completes one full cycle from \(0\) to \(2\pi\), indicating that the period is \(2\pi\).
- **Vertical Shift**: The graph oscillates around \(y = 0\), showing that there is no vertical shift.
- **Equation**: Based on the amplitude and period, a possible equation for the graph could be:
\[ y = 2 \cos\left(x\right) \]
#### b)
**Detailed Description**:
- **Type of Graph**: This appears to be a parabola opening downwards, suggesting it is a quadratic function.
- **Vertex**: The vertex of the parabola appears to be at the origin \((0,0)\).
- **Equation**: Since the parabola opens downward and appears to follow the basic quadratic form \(y = -ax^2\),
a possible equation for the graph could be:
\[ y = -x^2 \]
For further explanations on sinusoidal and quadratic functions, including how to determine their equations from graphs, please refer to the educational resources available on our website.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa55013e1-91aa-48be-9c4b-bf8a0e47de22%2F0b8b974d-07bc-4d4e-be9f-889ffbb8b7b3%2Fphr3ozy_processed.png&w=3840&q=75)
Transcribed Image Text:### Graph Analysis and Possible Equations
**Task**: Write a possible equation for the graphs below:
#### a)
**Detailed Description**:
- **Type of Graph**: This appears to be a sinusoidal graph, specifically a cosine graph.
- **Amplitude**: The maximum value is 2 and the minimum value is -2, suggesting that the amplitude is 2.
- **Period**: The graph completes one full cycle from \(0\) to \(2\pi\), indicating that the period is \(2\pi\).
- **Vertical Shift**: The graph oscillates around \(y = 0\), showing that there is no vertical shift.
- **Equation**: Based on the amplitude and period, a possible equation for the graph could be:
\[ y = 2 \cos\left(x\right) \]
#### b)
**Detailed Description**:
- **Type of Graph**: This appears to be a parabola opening downwards, suggesting it is a quadratic function.
- **Vertex**: The vertex of the parabola appears to be at the origin \((0,0)\).
- **Equation**: Since the parabola opens downward and appears to follow the basic quadratic form \(y = -ax^2\),
a possible equation for the graph could be:
\[ y = -x^2 \]
For further explanations on sinusoidal and quadratic functions, including how to determine their equations from graphs, please refer to the educational resources available on our website.
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