### Matching the Function with Its Graph: \( y = \sec(4x) \)To understand functions and their graphs, it's crucial to match the given function with the correct graph representation. Here, we will focus on matching the given function \( y = \sec(4x) \) with its correct graph out of the four provided.#### Graph Analysis OverviewThere are four graphs displayed, each representing a different function. Here is a detailed analysis of each graph:1. **Top-Left Graph:** - **Axes:** The graph features the x and y axes with key points marked at \( -\pi, -\frac{3\pi}{4}, -\frac{\pi}{2}, -\frac{\pi}{4}, 0, \frac{\pi}{4}, \frac{\pi}{2}, \frac{3\pi}{4}, \pi \) on the x-axis and standard integer points on the y-axis. - **Graphic Characteristics:** - Periodic vertical asymptotes. - Alternating upwards and downwards curvature from the asymptotes.2. **Top-Right Graph:** - **Axes:** The graph also features the x and y axes with intervals such as \( -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6 \) on the x-axis and integers on the y-axis. - **Graphic Characteristics:** - Flat horizontal lines combined with periodic vertical lines becoming asymptotes. - Alternating curvature from these asymptotes. 3. **Bottom-Left Graph:** - **Axes:** The x and y axes are marked similarly as the top-left graph. - **Graphic Characteristics:** - One large parabola-like structure. - Contains vertices at \(x = -\frac{3\pi}{4}, \frac{3\pi}{4} \, and \pi\).4. **Bottom-Right Graph:** - **Axes:** Clearly marked x and y axes with points spanning same specified intervals. - **Graphic Characteristics:** - Asymptotes at regular intervals and corresponding curved lines on either side of the asymptotes. - Should have periodicity that fits with secant function characteristics.#### Matching the Function \( y = \sec(

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Answered: Match the function with its graph. y =…

Match the function with its graph. y = sec(4x) JUU UL Зл MEN MA U 2 1 y ff म म Л Зл Зл 3A Зл 4 X 27 -2x 4 4 2 4 2 -1 -2 O KIN √5 + NOF KIN

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter1: Expressions And Functions

Section: Chapter Questions

Problem 74SGR

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Question

### Matching the Function with Its Graph: \( y = \sec(4x) \)

To understand functions and their graphs, it's crucial to match the given function with the correct graph representation. Here, we will focus on matching the given function \( y = \sec(4x) \) with its correct graph out of the four provided.

#### Graph Analysis Overview

There are four graphs displayed, each representing a different function. Here is a detailed analysis of each graph:

1. **Top-Left Graph:**
- **Axes:** The graph features the x and y axes with key points marked at \( -\pi, -\frac{3\pi}{4}, -\frac{\pi}{2}, -\frac{\pi}{4}, 0, \frac{\pi}{4}, \frac{\pi}{2}, \frac{3\pi}{4}, \pi \) on the x-axis and standard integer points on the y-axis.
- **Graphic Characteristics:**
- Periodic vertical asymptotes.
- Alternating upwards and downwards curvature from the asymptotes.

2. **Top-Right Graph:**
- **Axes:** The graph also features the x and y axes with intervals such as \( -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6 \) on the x-axis and integers on the y-axis.
- **Graphic Characteristics:**
- Flat horizontal lines combined with periodic vertical lines becoming asymptotes.
- Alternating curvature from these asymptotes.

3. **Bottom-Left Graph:**
- **Axes:** The x and y axes are marked similarly as the top-left graph.
- **Graphic Characteristics:**
- One large parabola-like structure.
- Contains vertices at \(x = -\frac{3\pi}{4}, \frac{3\pi}{4} \, and \pi\).

4. **Bottom-Right Graph:**
- **Axes:** Clearly marked x and y axes with points spanning same specified intervals.
- **Graphic Characteristics:**
- Asymptotes at regular intervals and corresponding curved lines on either side of the asymptotes.
- Should have periodicity that fits with secant function characteristics.

#### Matching the Function \( y = \sec(

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