Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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![**Function Analysis and Graphical Interpretation**
### Function
Given:
\[ f(x) = \frac{x^2 + 5x + 8}{x + 3} \]
### Graph
A coordinate plane is provided with grid lines ranging from \(-10\) to \(10\) on both the x-axis and the y-axis.
### Table for Analysis
| Hole(s) | Vertical Asymptote(s) | Horizontal Asymptote | Slant Asymptote | x-intercept(s) | y-intercept |
|---------|-----------------------|----------------------|-----------------|----------------|-------------|
| | | | | | |
### Notes
The table is intended for analyzing critical points of the function, such as:
- **Holes**: Points where the function is not defined due to factor cancellation.
- **Vertical Asymptotes**: Values of \(x\) that make the denominator zero and the function undefined.
- **Horizontal/Slant Asymptotes**: Asymptotes determined by the behavior of the function as \(x\) approaches infinity.
- **Intercepts**: Points where the function crosses the x-axis and y-axis.
This layout aids in thoroughly evaluating the function's properties and understanding its graphical representation.](https://content.bartleby.com/qna-images/question/d86db678-bc86-44fd-bd72-7c276c312ad6/dcb2767b-a038-4be2-b5a5-8e4b9a622270/wfpvr2k_processed.jpeg)
Transcribed Image Text:**Function Analysis and Graphical Interpretation**
### Function
Given:
\[ f(x) = \frac{x^2 + 5x + 8}{x + 3} \]
### Graph
A coordinate plane is provided with grid lines ranging from \(-10\) to \(10\) on both the x-axis and the y-axis.
### Table for Analysis
| Hole(s) | Vertical Asymptote(s) | Horizontal Asymptote | Slant Asymptote | x-intercept(s) | y-intercept |
|---------|-----------------------|----------------------|-----------------|----------------|-------------|
| | | | | | |
### Notes
The table is intended for analyzing critical points of the function, such as:
- **Holes**: Points where the function is not defined due to factor cancellation.
- **Vertical Asymptotes**: Values of \(x\) that make the denominator zero and the function undefined.
- **Horizontal/Slant Asymptotes**: Asymptotes determined by the behavior of the function as \(x\) approaches infinity.
- **Intercepts**: Points where the function crosses the x-axis and y-axis.
This layout aids in thoroughly evaluating the function's properties and understanding its graphical representation.
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