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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![**Transcription for Educational Website:**
**Title: Analyzing a Trigonometric Function**
**Instructions:**
Graph the function over a two-period interval.
**Function:**
\[ y = -2 - \frac{1}{2} \tan \left( 2 \left( x + \frac{3\pi}{2} \right) \right) \]
---
**Task:**
Choose the correct graph below that represents the given function.
**Options:**
- **A.**
- The graph shows two asymptotes at approximately \( x = -5\pi \) and \( x = 5\pi \).
- The graph spans vertically from -6 to 6 along the \( y \)-axis.
- It exhibits a characteristic tangent curve with decreasing intervals as it approaches the vertical asymptotes.
- **B.**
- The graph displays asymptotes at \( x = -9\pi \) and \( x = 5\pi \).
- The \( y \)-axis ranges from -6 to 6.
- It features sections of a tangent curve, moving downward across the intervals between asymptotes.
- **C.**
- There are vertical asymptotes at \( x = -2\pi \) and \( x = 1\).
- The graph expands from \( y = -6 \) to \( y = 6 \).
- It illustrates parts of a tangent function, moving upward between asymptotes.
**Note:**
Each graph is marked with a magnifying glass icon to zoom, and an expand icon for a full-screen view. Select the answer that corresponds correctly to the function provided.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb4d7178e-ae2a-4981-9b29-b3e3c6550ee0%2F7c864f15-ed0f-4354-a0a4-9c09a3e3f089%2Fs95rahd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Transcription for Educational Website:**
**Title: Analyzing a Trigonometric Function**
**Instructions:**
Graph the function over a two-period interval.
**Function:**
\[ y = -2 - \frac{1}{2} \tan \left( 2 \left( x + \frac{3\pi}{2} \right) \right) \]
---
**Task:**
Choose the correct graph below that represents the given function.
**Options:**
- **A.**
- The graph shows two asymptotes at approximately \( x = -5\pi \) and \( x = 5\pi \).
- The graph spans vertically from -6 to 6 along the \( y \)-axis.
- It exhibits a characteristic tangent curve with decreasing intervals as it approaches the vertical asymptotes.
- **B.**
- The graph displays asymptotes at \( x = -9\pi \) and \( x = 5\pi \).
- The \( y \)-axis ranges from -6 to 6.
- It features sections of a tangent curve, moving downward across the intervals between asymptotes.
- **C.**
- There are vertical asymptotes at \( x = -2\pi \) and \( x = 1\).
- The graph expands from \( y = -6 \) to \( y = 6 \).
- It illustrates parts of a tangent function, moving upward between asymptotes.
**Note:**
Each graph is marked with a magnifying glass icon to zoom, and an expand icon for a full-screen view. Select the answer that corresponds correctly to the function provided.
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