Which of the functions match the three graphs? ### Matching Graphs with Their EquationsThree graphs are shown below. Each graph represents one of the following equations. Choose the correct equation for each graph:\[ y = 2 \csc 2x \quad y = \tan x \quad y = \cot \left( x - \frac{\pi}{4} \right) \]\[ y = \csc \left( 2x + \frac{\pi}{2} \right) \quad y = \sec \left( 2x + \frac{\pi}{2} \right) \quad y = \tan \left( x + \frac{\pi}{4} \right) \]#### Graph Descriptions and Equations**Graph 1:**- **Description:** - This graph shows a periodic function with vertical asymptotes occurring periodically. There are vertical asymptotes at $ x = -\frac{3\pi}{4} $, $ x = -\frac{\pi}{4} $, $ x = \frac{\pi}{4} $, and $ x = \frac{3\pi}{4} $. The graph has its peaks and troughs mirrored across the x-axis, and the function transitions between the asymptotes smoothly.- **Equation:** - [Equation placeholder for users to input their answers]**Graph 2:**- **Description:** - This graph displays a function with vertical asymptotes at $ x = -\frac{\pi}{2} $, $ x = 0 $, and $ x = \frac{\pi}{2} $. There are symmetrical peaks and troughs between the asymptotes, typical of secant or cosecant functions.- **Equation:** - [Equation placeholder for users to input their answers]**Graph 3:**- **Description:** - The function represented in this graph has an infinite range with vertical asymptotes at $ x = -\pi $, $ x = -\frac{\pi}{2} $, $ x = 0 $, $ x = \frac{\pi}{2} $, and $ x = \pi $. The graph exhibits an S-shape curve between each set of asymptotes.- **Equation:** - [Equation placeholder for users to input their answers]Identify the correct equation for each graph based on their characteristics. Use

Answered: Image /qna-images/answer/5326a454-6dd3-4b7c-af60-d27acb491baa.jpg

Answered: Three graphs are given below. For each,…

Three graphs are given below. For each, choose its equation from the following. y = 2 csc 2x y = tanx y = cot x- y= csc 2x+ y= sec 2x+. y = tan x+- 2- %3D 4 %3D -2+ -2- 1.

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

Which of the functions match the three graphs?

### Matching Graphs with Their Equations

Three graphs are shown below. Each graph represents one of the following equations. Choose the correct equation for each graph:

\[ y = 2 \csc 2x \quad y = \tan x \quad y = \cot \left( x - \frac{\pi}{4} \right) \]
\[ y = \csc \left( 2x + \frac{\pi}{2} \right) \quad y = \sec \left( 2x + \frac{\pi}{2} \right) \quad y = \tan \left( x + \frac{\pi}{4} \right) \]

#### Graph Descriptions and Equations

**Graph 1:**

- **Description:**
- This graph shows a periodic function with vertical asymptotes occurring periodically. There are vertical asymptotes at $ x = -\frac{3\pi}{4} $, $ x = -\frac{\pi}{4} $, $ x = \frac{\pi}{4} $, and $ x = \frac{3\pi}{4} $. The graph has its peaks and troughs mirrored across the x-axis, and the function transitions between the asymptotes smoothly.
- **Equation:**
- [Equation placeholder for users to input their answers]

**Graph 2:**

- **Description:**
- This graph displays a function with vertical asymptotes at $ x = -\frac{\pi}{2} $, $ x = 0 $, and $ x = \frac{\pi}{2} $. There are symmetrical peaks and troughs between the asymptotes, typical of secant or cosecant functions.
- **Equation:**
- [Equation placeholder for users to input their answers]

**Graph 3:**

- **Description:**
- The function represented in this graph has an infinite range with vertical asymptotes at $ x = -\pi $, $ x = -\frac{\pi}{2} $, $ x = 0 $, $ x = \frac{\pi}{2} $, and $ x = \pi $. The graph exhibits an S-shape curve between each set of asymptotes.
- **Equation:**
- [Equation placeholder for users to input their answers]

Identify the correct equation for each graph based on their characteristics. Use

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