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 asymptotes.
Let's understand the concept better.
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:
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 x = 3.
NOTE: The numerator of the function cannot be equal to 0.