Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Question
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![**Task: Graph Two Periods of the Given Tangent Function**
**Function:**
\[ y = \tan\left(x - \frac{\pi}{6}\right) \]
**Instructions:**
Choose the correct graph of two periods for the function \( y = \tan\left(x - \frac{\pi}{6}\right) \) from the options below.
**Graph Options:**
**A.**
- The graph displays two periods of a tangent function.
- Asymptotes appear around \(x = -\frac{\pi}{3}\), \(\frac{\pi}{3}\), and \(\frac{5\pi}{3}\).
- The function crosses the x-axis near \(x = \frac{\pi}{6}\).
**B.**
- The graph shows two periods of a tangent function.
- Asymptotes occur around \(x = \frac{\pi}{3}\), \(\pi\), and \(\frac{4\pi}{3}\).
- The function crosses the x-axis around \(x = \frac{7\pi}{6}\).
**C.**
- The graph depicts two periods of a tangent function.
- Asymptotes can be observed approximately at \(x = \frac{\pi}{2}\), \(\frac{3\pi}{2}\), and \(\frac{5\pi}{2}\).
- The function crosses the x-axis approximately at \(x = \frac{5\pi}{6}\).
**D.**
- The graph presents two periods of a tangent function.
- Asymptotes appear around \(x = 0\), \(\pi\), and \(2\pi\).
- The function crosses the x-axis around \(x = \frac{\pi}{6}\).
**Note:**
When identifying the correct graph:
- Consider the horizontal shift of the tangent function due to \(x - \frac{\pi}{6}\).
- Look for the correct positioning of asymptotes and x-intercepts relative to this transformation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9fe330d6-ed92-43b3-9547-c6e2b1ed5b0a%2Faa3ea4ec-1020-4e1d-b250-f06845d44f45%2Fag58iwt_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Task: Graph Two Periods of the Given Tangent Function**
**Function:**
\[ y = \tan\left(x - \frac{\pi}{6}\right) \]
**Instructions:**
Choose the correct graph of two periods for the function \( y = \tan\left(x - \frac{\pi}{6}\right) \) from the options below.
**Graph Options:**
**A.**
- The graph displays two periods of a tangent function.
- Asymptotes appear around \(x = -\frac{\pi}{3}\), \(\frac{\pi}{3}\), and \(\frac{5\pi}{3}\).
- The function crosses the x-axis near \(x = \frac{\pi}{6}\).
**B.**
- The graph shows two periods of a tangent function.
- Asymptotes occur around \(x = \frac{\pi}{3}\), \(\pi\), and \(\frac{4\pi}{3}\).
- The function crosses the x-axis around \(x = \frac{7\pi}{6}\).
**C.**
- The graph depicts two periods of a tangent function.
- Asymptotes can be observed approximately at \(x = \frac{\pi}{2}\), \(\frac{3\pi}{2}\), and \(\frac{5\pi}{2}\).
- The function crosses the x-axis approximately at \(x = \frac{5\pi}{6}\).
**D.**
- The graph presents two periods of a tangent function.
- Asymptotes appear around \(x = 0\), \(\pi\), and \(2\pi\).
- The function crosses the x-axis around \(x = \frac{\pi}{6}\).
**Note:**
When identifying the correct graph:
- Consider the horizontal shift of the tangent function due to \(x - \frac{\pi}{6}\).
- Look for the correct positioning of asymptotes and x-intercepts relative to this transformation.
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