Graph the rational function. -4x-18x-12 f(x)= 6x+9 Start by drawing the asymptotes. Then plot two points on each piece of the graph. Finally, click on the graph-a-functior 10- -10 -10- Check Explanation 2021 McGraw --..
Graph the rational function. -4x-18x-12 f(x)= 6x+9 Start by drawing the asymptotes. Then plot two points on each piece of the graph. Finally, click on the graph-a-functior 10- -10 -10- Check Explanation 2021 McGraw --..
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
Need help on where to place the asymptote
![**Graphing a Rational Function**
To graph the rational function given by
\[
f(x) = \frac{-4x^2 - 18x - 12}{6x + 9}
\]
follow these steps:
1. **Identify Asymptotes**: First, identify the vertical and horizontal asymptotes. This step is crucial for understanding the behavior of the graph.
2. **Plotting Points**: After determining the asymptotes, select two points on each segment of the graph. This helps in defining the curve accurately.
3. **Drawing the Graph**: Use the graph-a-function button to complete the graph once the critical points and asymptotes are plotted.
**Graph Description:**
- The grid shown is a Cartesian plane with x and y axes ranging from -10 to 10.
- There are tools visible on the right side used for plotting: a pencil, line, curve, and other graphing utilities.
- The bottom buttons include options for "Explanation" and "Check".
This structured approach ensures you understand each element of graphing a rational function step-by-step.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3899185f-2e74-4a69-b98e-bc78fbd80797%2F9ee4c0ee-8c0f-4e51-bbf1-781319e97e03%2Fnx1ehz_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Graphing a Rational Function**
To graph the rational function given by
\[
f(x) = \frac{-4x^2 - 18x - 12}{6x + 9}
\]
follow these steps:
1. **Identify Asymptotes**: First, identify the vertical and horizontal asymptotes. This step is crucial for understanding the behavior of the graph.
2. **Plotting Points**: After determining the asymptotes, select two points on each segment of the graph. This helps in defining the curve accurately.
3. **Drawing the Graph**: Use the graph-a-function button to complete the graph once the critical points and asymptotes are plotted.
**Graph Description:**
- The grid shown is a Cartesian plane with x and y axes ranging from -10 to 10.
- There are tools visible on the right side used for plotting: a pencil, line, curve, and other graphing utilities.
- The bottom buttons include options for "Explanation" and "Check".
This structured approach ensures you understand each element of graphing a rational function step-by-step.
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