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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Question
![**Graphing Tangent Functions**
**Objective:**
Graph two periods of the given tangent function.
Given Function:
\[ y = \tan\left(x - \frac{\pi}{4}\right) \]
**Task:**
Choose the correct graph of two periods of \( y = \tan\left(x - \frac{\pi}{4}\right) \) from the options below.
**Graph Options:**
- **Option A:**
- Features two tangent curves.
- The first curve spans from \( -\frac{\pi}{2} \) to \( \frac{\pi}{2} \).
- Asymptotes occur at \( x = -\frac{\pi}{2} \) and \( x = \frac{\pi}{2} \).
- The second period follows similarly after a repeat.
- **Option B:**
- Exhibits similar features with a different phase shift.
- Asymptotes occur at \( x = 0 \) and \( x = \pi \).
- **Option C:**
- Two periods shown with asymptotes at \( x = \frac{\pi}{4} \) and \( x = \frac{5\pi}{4} \).
- Graph shifts the tangent curve horizontally by \(\frac{\pi}{4}\).
- **Option D:**
- Consists of similarly distributed tangent curves.
- Asymptotes are at \( x = -\frac{\pi}{4} \) and \( x = \frac{3\pi}{4} \).
The correct choice would typically involve identifying the horizontal shift of \(\frac{\pi}{4}\) to the right as indicated in the function \( y = \tan\left(x - \frac{\pi}{4}\right) \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3e0c8ff2-4587-423f-8b9a-06c9b1ec5275%2F9f6547c7-4a79-4a1d-b206-33d4d3be4a0c%2Flykc5se_processed.png&w=3840&q=75)
Transcribed Image Text:**Graphing Tangent Functions**
**Objective:**
Graph two periods of the given tangent function.
Given Function:
\[ y = \tan\left(x - \frac{\pi}{4}\right) \]
**Task:**
Choose the correct graph of two periods of \( y = \tan\left(x - \frac{\pi}{4}\right) \) from the options below.
**Graph Options:**
- **Option A:**
- Features two tangent curves.
- The first curve spans from \( -\frac{\pi}{2} \) to \( \frac{\pi}{2} \).
- Asymptotes occur at \( x = -\frac{\pi}{2} \) and \( x = \frac{\pi}{2} \).
- The second period follows similarly after a repeat.
- **Option B:**
- Exhibits similar features with a different phase shift.
- Asymptotes occur at \( x = 0 \) and \( x = \pi \).
- **Option C:**
- Two periods shown with asymptotes at \( x = \frac{\pi}{4} \) and \( x = \frac{5\pi}{4} \).
- Graph shifts the tangent curve horizontally by \(\frac{\pi}{4}\).
- **Option D:**
- Consists of similarly distributed tangent curves.
- Asymptotes are at \( x = -\frac{\pi}{4} \) and \( x = \frac{3\pi}{4} \).
The correct choice would typically involve identifying the horizontal shift of \(\frac{\pi}{4}\) to the right as indicated in the function \( y = \tan\left(x - \frac{\pi}{4}\right) \).
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