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...
Related questions
Question
what is the graph and what is the period?
Please show easy step by step thank you
![**Match the Function with Its Graph**
**Given Function:**
\[ y = \tan \left( \frac{x}{2} \right) \]
**Explanation of Graphs:**
1. **Top-Left Graph:**
- This graph shows vertical asymptotes at \( x = -\pi \) and \( x = \pi \).
- The function increases rapidly, showing the characteristic shape of the tangent function.
- The curves approach the vertical asymptotes from opposite sides.
2. **Top-Right Graph:**
- This graph displays a periodic nature with vertical asymptotes at \( x = -\frac{\pi}{2} \) and \( x = \frac{\pi}{2} \).
- The graph appears to represent a function that repeats between these asymptotes.
3. **Bottom-Left Graph:**
- This graph shows multiple vertical asymptotes between \( x = -5 \) and \( x = 5 \).
- The function appears to have more frequent vertical asymptotes, indicating a periodic function with a shorter period.
4. **Bottom-Right Graph (Correct Answer):**
- The graph has vertical asymptotes at \( x = -\frac{\pi}{2} \) and \( x = \frac{\pi}{2} \), which fits the period of the tangent function when scaled by a factor of 2.
- The behavior of the graph matches the behavior of the tangent function: increasing steeply between the vertical asymptotes.
**Conclusion:**
For the function \( y = \tan \left( \frac{x}{2} \right) \), the correct graph is the **Bottom-Right Graph** with the vertical asymptotes at \( x = -\frac{\pi}{2} \) and \( x = \frac{\pi}{2} \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa0e38307-1ade-44bc-b712-aaeda4c58098%2F1155d37a-759c-4ec1-b38d-01edf7b94b22%2Fkqwpm39_processed.png&w=3840&q=75)
Transcribed Image Text:**Match the Function with Its Graph**
**Given Function:**
\[ y = \tan \left( \frac{x}{2} \right) \]
**Explanation of Graphs:**
1. **Top-Left Graph:**
- This graph shows vertical asymptotes at \( x = -\pi \) and \( x = \pi \).
- The function increases rapidly, showing the characteristic shape of the tangent function.
- The curves approach the vertical asymptotes from opposite sides.
2. **Top-Right Graph:**
- This graph displays a periodic nature with vertical asymptotes at \( x = -\frac{\pi}{2} \) and \( x = \frac{\pi}{2} \).
- The graph appears to represent a function that repeats between these asymptotes.
3. **Bottom-Left Graph:**
- This graph shows multiple vertical asymptotes between \( x = -5 \) and \( x = 5 \).
- The function appears to have more frequent vertical asymptotes, indicating a periodic function with a shorter period.
4. **Bottom-Right Graph (Correct Answer):**
- The graph has vertical asymptotes at \( x = -\frac{\pi}{2} \) and \( x = \frac{\pi}{2} \), which fits the period of the tangent function when scaled by a factor of 2.
- The behavior of the graph matches the behavior of the tangent function: increasing steeply between the vertical asymptotes.
**Conclusion:**
For the function \( y = \tan \left( \frac{x}{2} \right) \), the correct graph is the **Bottom-Right Graph** with the vertical asymptotes at \( x = -\frac{\pi}{2} \) and \( x = \frac{\pi}{2} \).
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 1 images
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning