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Answer
The vertical asymptote is at
Solution
Find the vertical asymptotes of the function
Function by following steps:
Function by following steps:
- step0: Find the vertical asymptotes:
- step1: Evaluate the limit:
- step2: Evaluate the left-hand and the right-hand limits:
- step3: Evaluate the left-hand limit:
- step4: Limit does not exist:
- step5:
is a vertical asymptote
- step6: List all vertical asymptotes of the function:
The vertical asymptote of the functionis at .
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Did you know that the equation you provided represents a rational function? These types of functions can often showcase fascinating behaviors like asymptotes and intercepts! For instance, when we examine
When working with rational functions, a common mistake is forgetting to factor both the numerator and the denominator completely. This can lead to missing out on simplifying the expression or identifying any potential holes in the graph where the function is undefined. Always double-check your work for any common factors that might need canceling!
