Match the trigonometric function with one of the graphs I-VI. f(x) = tan x + ---Select-- v II III 37 5m 4! TT IV VI 2- 1- TT 37 X ------
Match the trigonometric function with one of the graphs I-VI. f(x) = tan x + ---Select-- v II III 37 5m 4! TT IV VI 2- 1- TT 37 X ------
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
![**Title: Matching Trigonometric Functions to Graphs**
**Instructions:**
Match the trigonometric function with one of the graphs I-VI.
**Trigonometric Function:**
\[ f(x) = \tan\left(x + \frac{\pi}{4}\right) \]
**Graph Options:**
**Graph I:**
- **Axes:** y-axis and x-axis.
- **Intervals:** Vertical asymptotes at \(x = -\frac{\pi}{2}\) and \(x = \pi\).
- **Behavior:** The curve passes through the origin \((0, 0)\) and moves upwards to the right, with a vertical asymptote at \(x = \pi\).
**Graph II:**
- **Axes:** y-axis and x-axis.
- **Intervals:** Vertical asymptotes at \(x = \frac{\pi}{4}\), \(x = \frac{3\pi}{4}\), and \(x = \frac{5\pi}{4}\).
- **Behavior:** Characteristic upward slope of tangent, passing through \((0, -1)\).
**Graph III:**
- **Axes:** y-axis and x-axis.
- **Intervals:** Vertical asymptotes at \(x = \frac{\pi}{4}\), \(x = \frac{7\pi}{4}\).
- **Behavior:** Multiple sections, showing periodic pattern of tangent, opening upwards and downwards.
**Graph IV:**
- **Axes:** y-axis and x-axis.
- **Intervals:** Vertical asymptotes at \(x = -\frac{\pi}{2}\), \(x = \frac{3\pi}{2}\).
- **Behavior:** U-shape curves, periodic, repeating every section.
**Graph V:**
- **Axes:** y-axis and x-axis.
- **Intervals:** Vertical asymptotes at \(x = -\frac{\pi}{2}\), \(x = \frac{\pi}{2}\), \(x = \frac{3\pi}{2}\).
- **Behavior:** Smooth increasing curve passing through \((0, 0)\), following a periodic pattern.
**Graph VI:**
- **Axes:** y-axis and x-axis.
- **Intervals:** Vertical asymptotes at \(x = \frac{\pi}{4}\) and \(x = \frac{7\pi}{4}\).
- **Behavior:** Features multiple sections](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb8492a80-fb1a-4bc0-8e68-f5fde27cb209%2F0d41f8d1-87e0-41d4-aecf-62379852cf8c%2Fnmy4tz_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Matching Trigonometric Functions to Graphs**
**Instructions:**
Match the trigonometric function with one of the graphs I-VI.
**Trigonometric Function:**
\[ f(x) = \tan\left(x + \frac{\pi}{4}\right) \]
**Graph Options:**
**Graph I:**
- **Axes:** y-axis and x-axis.
- **Intervals:** Vertical asymptotes at \(x = -\frac{\pi}{2}\) and \(x = \pi\).
- **Behavior:** The curve passes through the origin \((0, 0)\) and moves upwards to the right, with a vertical asymptote at \(x = \pi\).
**Graph II:**
- **Axes:** y-axis and x-axis.
- **Intervals:** Vertical asymptotes at \(x = \frac{\pi}{4}\), \(x = \frac{3\pi}{4}\), and \(x = \frac{5\pi}{4}\).
- **Behavior:** Characteristic upward slope of tangent, passing through \((0, -1)\).
**Graph III:**
- **Axes:** y-axis and x-axis.
- **Intervals:** Vertical asymptotes at \(x = \frac{\pi}{4}\), \(x = \frac{7\pi}{4}\).
- **Behavior:** Multiple sections, showing periodic pattern of tangent, opening upwards and downwards.
**Graph IV:**
- **Axes:** y-axis and x-axis.
- **Intervals:** Vertical asymptotes at \(x = -\frac{\pi}{2}\), \(x = \frac{3\pi}{2}\).
- **Behavior:** U-shape curves, periodic, repeating every section.
**Graph V:**
- **Axes:** y-axis and x-axis.
- **Intervals:** Vertical asymptotes at \(x = -\frac{\pi}{2}\), \(x = \frac{\pi}{2}\), \(x = \frac{3\pi}{2}\).
- **Behavior:** Smooth increasing curve passing through \((0, 0)\), following a periodic pattern.
**Graph VI:**
- **Axes:** y-axis and x-axis.
- **Intervals:** Vertical asymptotes at \(x = \frac{\pi}{4}\) and \(x = \frac{7\pi}{4}\).
- **Behavior:** Features multiple sections
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