Algebra and Trigonometry (6th Edition)
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.
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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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