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.
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.
Transcribed Image Text:### 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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![### 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](https://content.bartleby.com/qna-images/question/38188fd7-32af-4cc1-9ec8-e56982db8708/5326a454-6dd3-4b7c-af60-d27acb491baa/6rjrxwc.png)
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