**Title: Analyzing Intercepts and Asymptotes****Instructions:**From the graph, determine the x– and y-intercepts and the vertical and horizontal asymptotes. (If an answer does not exist, enter DNE. Enter your asymptotes as a comma-separated list of equations if necessary.)**Intercepts and Asymptotes:**- **X-Intercept (smaller x-value):** \[ (x, y) = \left( \ \ \ \ \ \right) \]- **X-Intercept (larger x-value):** \[ (x, y) = \left( \ \ \ \ \ \right) \]- **Y-Intercept:** \[ (x, y) = \left( \ \ \ \ \ \right) \]- **Vertical Asymptote(s):** \[ \ \ \ \ \ \ \]- **Horizontal Asymptote:** \[ \ \ \ \ \ \ \]**Graph Description:**A two-dimensional graph is provided with the following characteristics:- **X-Axis:** This horizontal axis is labeled with values ranging from -6 to 6.- **Y-Axis:** This vertical axis is labeled with values ranging from -6 to 6.- **Graph of the Function:** The function appears in red. It approaches the x-axis but never touches it, indicating a vertical asymptote at some points. Notably, the function dips into negative y-values and appears to have a local minimum point before rising again, touching or crossing the x-axis at two distinct points and approaching a horizontal asymptote.- **Horizontal Asymptote:** A dashed blue horizontal line represents the horizontal asymptote, intersecting the y-axis at y = 2. By closely analyzing the slopes and intersections, one can determine the specifics of the x- and y-intercepts, as well as the equations of the asymptotes. Ensure to consider these points carefully and enter the values and equations as required.

Answered: Image /qna-images/answer/f7338b0d-ec77-4567-9b51-4d8e4e85f802.jpg

From the graph, determine the x- and y-intercepts and the vertical and horizontal asymptotes. (If an answer does not exist, enter DNE. Enter your asymptotes as a comma-separated list of equations if nece (x, y) = ( (smaller x-value) x-intercept (x, y) = ( (larger x-value) хintercept y-intercept (x. y) = vertical asymptote(s) horizontal asymptote y 6 -6 -4 -2 2. 4 2.

From the graph, determine the x- and y-intercepts and the vertical and horizontal asymptotes. (If an answer does not exist, enter DNE. Enter your asymptotes as a comma-separated list of equations if nece (x, y) = ( (smaller x-value) x-intercept (x, y) = ( (larger x-value) хintercept y-intercept (x. y) = vertical asymptote(s) horizontal asymptote y 6 -6 -4 -2 2. 4 2.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.5: Graphs Of Functions

Problem 38E

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Question

**Title: Analyzing Intercepts and Asymptotes**

**Instructions:**
From the graph, determine the x– and y-intercepts and the vertical and horizontal asymptotes. (If an answer does not exist, enter DNE. Enter your asymptotes as a comma-separated list of equations if necessary.)

**Intercepts and Asymptotes:**

- **X-Intercept (smaller x-value):**
\[
(x, y) = \left( \ \ \ \ \ \right)
\]

- **X-Intercept (larger x-value):**
\[
(x, y) = \left( \ \ \ \ \ \right)
\]

- **Y-Intercept:**
\[
(x, y) = \left( \ \ \ \ \ \right)
\]

- **Vertical Asymptote(s):**
\[
\ \ \ \ \ \
\]

- **Horizontal Asymptote:**
\[
\ \ \ \ \ \
\]

**Graph Description:**
A two-dimensional graph is provided with the following characteristics:

- **X-Axis:** This horizontal axis is labeled with values ranging from -6 to 6.
- **Y-Axis:** This vertical axis is labeled with values ranging from -6 to 6.
- **Graph of the Function:** The function appears in red. It approaches the x-axis but never touches it, indicating a vertical asymptote at some points. Notably, the function dips into negative y-values and appears to have a local minimum point before rising again, touching or crossing the x-axis at two distinct points and approaching a horizontal asymptote.
- **Horizontal Asymptote:** A dashed blue horizontal line represents the horizontal asymptote, intersecting the y-axis at y = 2.

By closely analyzing the slopes and intersections, one can determine the specifics of the x- and y-intercepts, as well as the equations of the asymptotes. Ensure to consider these points carefully and enter the values and equations as required.

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