Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![### Finding the Vertical Asymptote
To determine the vertical asymptote for a given rational function, we need to find the values of \( x \) that make the denominator equal to zero (since division by zero is undefined).
Consider the following problem and its multiple-choice answers:
**Problem:**
Find the value of the vertical asymptote for the function:
\[ \frac{2x^2 - 3x + 5}{x - 9} \]
**Possible Answers:**
- \( -3 \)
- \( -9 \)
- \( 3 \)
- \( 9 \)
### Explanation:
In the rational function \( \frac{2x^2 - 3x + 5}{x - 9} \), the denominator is \( x - 9 \).
To find the vertical asymptote, set the denominator equal to zero:
\[ x - 9 = 0 \]
Solving for \( x \):
\[ x = 9 \]
Thus, the vertical asymptote occurs where \( x = 9 \).
**Answer:**
The value of the vertical asymptote is \(\boxed{9}\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb02aa80b-8f4b-476a-a9e7-a7b0f488ba00%2F40907f62-0532-4fe7-90c8-05fb4289965f%2Fa49a2s_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Finding the Vertical Asymptote
To determine the vertical asymptote for a given rational function, we need to find the values of \( x \) that make the denominator equal to zero (since division by zero is undefined).
Consider the following problem and its multiple-choice answers:
**Problem:**
Find the value of the vertical asymptote for the function:
\[ \frac{2x^2 - 3x + 5}{x - 9} \]
**Possible Answers:**
- \( -3 \)
- \( -9 \)
- \( 3 \)
- \( 9 \)
### Explanation:
In the rational function \( \frac{2x^2 - 3x + 5}{x - 9} \), the denominator is \( x - 9 \).
To find the vertical asymptote, set the denominator equal to zero:
\[ x - 9 = 0 \]
Solving for \( x \):
\[ x = 9 \]
Thus, the vertical asymptote occurs where \( x = 9 \).
**Answer:**
The value of the vertical asymptote is \(\boxed{9}\).
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