
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN: 9780134463216
Author: Robert F. Blitzer
Publisher: PEARSON
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![**Title: Understanding Vertical Asymptotes and Holes in Rational Functions**
**Objective:** Learn how to identify vertical asymptotes and holes in the graph of a rational function.
**Problem Statement:**
Find the vertical asymptotes, if any, and the values of \(x\) corresponding to holes, if any, in the graph of the rational function:
\[ h(x) = \frac{x}{x(x + 4)} \]
**Instructions:**
Select the correct choice below and, if necessary, fill in the answer box to complete your choice. (Type an equation. Use commas to separate answers as needed.)
**Options:**
- **A:** The vertical asymptote(s) is (are) [ ] . There are no holes.
- **B:** The vertical asymptote(s) is (are) [ ] and hole(s) corresponding to [ ] .
- **C:** There are no vertical asymptotes but there is (are) hole(s) corresponding to [ ] .
- **D:** There are no discontinuities.
**Additional Help:**
- Use "Help me solve this" for step-by-step guidance.
- Check out "View an example" for a similar problem.
- Click on "Get more help" for additional resources.
**Note:**
This task emphasizes understanding the nature of rational functions by identifying points of discontinuity. A vertical asymptote occurs where the function is undefined and does not cancel, while a hole occurs where factors cancel out in the rational expression.](https://content.bartleby.com/qna-images/question/a4643730-756f-4385-a96d-a4c90bcc91eb/60d49a0e-093f-4bf3-bf4b-0d607a46fea5/bvfkikg_thumbnail.jpeg)
Transcribed Image Text:**Title: Understanding Vertical Asymptotes and Holes in Rational Functions**
**Objective:** Learn how to identify vertical asymptotes and holes in the graph of a rational function.
**Problem Statement:**
Find the vertical asymptotes, if any, and the values of \(x\) corresponding to holes, if any, in the graph of the rational function:
\[ h(x) = \frac{x}{x(x + 4)} \]
**Instructions:**
Select the correct choice below and, if necessary, fill in the answer box to complete your choice. (Type an equation. Use commas to separate answers as needed.)
**Options:**
- **A:** The vertical asymptote(s) is (are) [ ] . There are no holes.
- **B:** The vertical asymptote(s) is (are) [ ] and hole(s) corresponding to [ ] .
- **C:** There are no vertical asymptotes but there is (are) hole(s) corresponding to [ ] .
- **D:** There are no discontinuities.
**Additional Help:**
- Use "Help me solve this" for step-by-step guidance.
- Check out "View an example" for a similar problem.
- Click on "Get more help" for additional resources.
**Note:**
This task emphasizes understanding the nature of rational functions by identifying points of discontinuity. A vertical asymptote occurs where the function is undefined and does not cancel, while a hole occurs where factors cancel out in the rational expression.
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