How to find Vertical Asymptotes?
Vertical lines that correspond to the zeros of the denominator of a rational function are known as vertical asymptotes.
Answer: By solving the equation f(x) = 0, where f(x) is the denominator of a rational function we can find the vertical asymptote.
A vertical asymptote is a vertical line that corresponds to the zeros of the denominator of a polynomial function.
Let us take an example of a graph, and explain the purpose of having a vertical asymptote.
Look at the diagram given below:
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In the above graph, the function has avoided vales at x = 6 and x = -1, since the zeros at that point were undefined or discontinuous, thus our possible asymptotes are at x = 6, -1.
Let us take the help of an example to better understand the concept.
Example: Find the vertical asymptote of f(x) = 1 / x-3
Solution: According to our definition, let's equate the denominator to 0.
x - 3 = 0.
x = 3.
The graph has a vertical asymptote with x = 3.
NOTE: The numerator of the function cannot be equal to 0.