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
How do you draw this graph and how do you determine the undefined when period changes ?
![**Equation and Transformations:**
The given equation is:
\[ y = -2 \tan \left(\frac{x}{4} + \frac{\pi}{2}\right) = -2 \tan \frac{1}{4}(x + 2\pi) \]
- **Vertical Reflection:** The negative sign reflects the graph vertically.
- **Vertical Stretch:** The factor of 2 stretches the graph vertically by 2.
- **Amplitude (A):** Not applicable (N/A) for tangent functions.
- **Period (p):** Calculated as \( \pi \times 4 = 4\pi \).
- **Horizontal Shift (HS):** The graph is shifted \( 2\pi \) to the left.
**Graph:**
The graph represents the tangent function described above:
- **Axes:**
- The vertical axis (y-axis) ranges from -2 to 2.
- The horizontal axis (x-axis) is labeled from \(-4\pi\) to \(-\pi\) in increments of \(\pi\).
The graph illustrates a transformed tangent function with a vertical reflection and stretch, along with horizontal translation. The period of the function is \(4\pi\), indicating the distance required for the function to start repeating.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff4116597-78e6-477d-91b2-9fa4cad4d0f7%2F6d5d06c8-dbc8-481f-bb27-2875c1508d86%2Flarjs5n_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Equation and Transformations:**
The given equation is:
\[ y = -2 \tan \left(\frac{x}{4} + \frac{\pi}{2}\right) = -2 \tan \frac{1}{4}(x + 2\pi) \]
- **Vertical Reflection:** The negative sign reflects the graph vertically.
- **Vertical Stretch:** The factor of 2 stretches the graph vertically by 2.
- **Amplitude (A):** Not applicable (N/A) for tangent functions.
- **Period (p):** Calculated as \( \pi \times 4 = 4\pi \).
- **Horizontal Shift (HS):** The graph is shifted \( 2\pi \) to the left.
**Graph:**
The graph represents the tangent function described above:
- **Axes:**
- The vertical axis (y-axis) ranges from -2 to 2.
- The horizontal axis (x-axis) is labeled from \(-4\pi\) to \(-\pi\) in increments of \(\pi\).
The graph illustrates a transformed tangent function with a vertical reflection and stretch, along with horizontal translation. The period of the function is \(4\pi\), indicating the distance required for the function to start repeating.
Expert Solution
Step 1
Put given values of x in the given function and draw the corresponding y value on the graph.
Step by step
Solved in 3 steps with 2 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.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