y = -2 - tanx + 4
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE:
1. Give the measures of the complement and the supplement of an angle measuring 35°.
Related questions
Question
![### Transcription for Educational Website:
**Problem 20:**
\[ y = -2 - \tan \left( x + \frac{\pi}{4} \right) \]
**Graph Description:**
The graph displays a coordinate plane with the x-axis and y-axis. Both axes are marked with evenly spaced tick marks representing unit intervals.
**Analysis of the Function:**
- **Function**: The equation describes a transformation of the tangent function.
- **Translation**: The horizontal translation is by \(-\frac{\pi}{4}\), shifting the graph to the left.
- **Vertical Shift**: The graph is shifted downward by 2 units, indicated by \(-2\).
- **Periodicity**: The tangent function has a period of \(\pi\), so the graph will repeat every \(\pi\) units along the x-axis.
- **Asymptotes**: As with all tangent functions, there will be vertical asymptotes, the placement of which will be modified by the function's transformation.
Understanding these transformations will help in accurately graphing and analyzing the function's behavior on the coordinate plane provided.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2f9e96de-8215-4532-a7d0-6f1fdf87f241%2F4902288f-6bab-4683-b774-7272ec8c4fea%2Fm08hrtv_processed.png&w=3840&q=75)
Transcribed Image Text:### Transcription for Educational Website:
**Problem 20:**
\[ y = -2 - \tan \left( x + \frac{\pi}{4} \right) \]
**Graph Description:**
The graph displays a coordinate plane with the x-axis and y-axis. Both axes are marked with evenly spaced tick marks representing unit intervals.
**Analysis of the Function:**
- **Function**: The equation describes a transformation of the tangent function.
- **Translation**: The horizontal translation is by \(-\frac{\pi}{4}\), shifting the graph to the left.
- **Vertical Shift**: The graph is shifted downward by 2 units, indicated by \(-2\).
- **Periodicity**: The tangent function has a period of \(\pi\), so the graph will repeat every \(\pi\) units along the x-axis.
- **Asymptotes**: As with all tangent functions, there will be vertical asymptotes, the placement of which will be modified by the function's transformation.
Understanding these transformations will help in accurately graphing and analyzing the function's behavior on the coordinate plane provided.
Expert Solution
Step 1: Consider the provided function,
Step by step
Solved in 2 steps with 3 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, trigonometry and related others by exploring similar questions and additional content below.Recommended textbooks for you
Trigonometry (11th Edition)
Trigonometry
ISBN:
9780134217437
Author:
Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:
PEARSON
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781305652224
Author:
Charles P. McKeague, Mark D. Turner
Publisher:
Cengage Learning
Trigonometry (11th Edition)
Trigonometry
ISBN:
9780134217437
Author:
Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:
PEARSON
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781305652224
Author:
Charles P. McKeague, Mark D. Turner
Publisher:
Cengage Learning
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781337278461
Author:
Ron Larson
Publisher:
Cengage Learning