Math Problem Statement
Solution
The given function is:
The vertical asymptote of a rational function occurs when the denominator is equal to zero, and the function becomes undefined.
For , the denominator gives:
So, the original function has a vertical asymptote at .
The question is about finding the vertical asymptote of the function .
Let's rewrite the function :
To find the vertical asymptote, set the denominator to zero:
Solving for :
Thus, the equation of the vertical asymptote of is:
Would you like more details on the steps involved or have any questions?
Here are some related questions you might consider:
- What is a vertical asymptote, and why does it occur in rational functions?
- How does the transformation affect the graph of a function?
- How do you find horizontal asymptotes of rational functions?
- What happens to the asymptotes if you multiply or divide the function by a constant?
- How do you determine the behavior of a function near its asymptotes?
Tip: To find vertical asymptotes, always look for the values of that make the denominator zero, since the function is undefined there.
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Math Problem Analysis
Mathematical Concepts
Rational Functions
Vertical Asymptotes
Function Transformations
Formulas
The vertical asymptote occurs when the denominator of a rational function equals zero
Theorems
Vertical Asymptote Theorem
Function Transformation (r(ax))
Suitable Grade Level
Grades 10-12
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