Math Problem Statement
Find the vertical asymptotes. Select the correct choice below and fill in any answer boxes within your choice.
A.
The vertical asymptote(s) can be described by the line(s)
enter your response here.
(Type an equation. Use a comma to separate answers as needed.)
B.
There are no vertical asymptotes.
Solution
To find the vertical asymptotes of the function , follow these steps:
Step 1: Identify potential vertical asymptotes.
- Vertical asymptotes occur where the denominator of a rational function is equal to zero (and the numerator is non-zero at that point).
Step 2: Set the denominator equal to zero.
- The denominator of is .
Set the denominator equal to zero and solve for :
Conclusion:
- There is a vertical asymptote at .
Choice A is the correct answer:
- The vertical asymptote(s) can be described by the line .
Would you like further details on this, or do you have any other questions? Here are five related questions:
- What happens to as approaches from the left and right?
- Can a function have more than one vertical asymptote?
- How does the presence of vertical asymptotes affect the graph of a function?
- What is the difference between a vertical asymptote and a hole in the graph?
- How do you determine if a vertical asymptote exists using limits?
Tip: Vertical asymptotes represent values of where the function becomes undefined and the function value tends to .
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Math Problem Analysis
Mathematical Concepts
Functions
Rational Functions
Vertical Asymptotes
Formulas
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Theorems
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Suitable Grade Level
High School
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