Vertical Asmptote
If one side of the limit approaches infinity usually in 1/x kind of functions, rational functionsin 1/(1-x) x=1 would be a VA
In mathematics, a vertical asymptote is a vertical line that a curve approaches but never touches or crosses as it extends towards infinity or negative infinity. It is a point on a curve, where the function approaches infinity or negative infinity. A vertical asymptote can occur where the denominator of a rational function becomes zero, leading to an undefined expression, or where a function approaches a limit as x approaches some specific value.
For example, the function f(x) = 1 / (x – 3) has a vertical asymptote at x = 3 because the denominator becomes zero at that point. As x approaches 3 from either side, the function becomes increasingly large (either positive or negative), but it never touches or crosses the vertical line x = 3. Similarly, the function g(x) = sqrt(x + 1) / (x – 2) approaches infinity as x approaches 2, so there is a vertical asymptote at x = 2.
Vertical asymptotes can be useful in graphing functions, as they help us understand the behavior of the function as x approaches certain values. It’s important to note that not all functions have vertical asymptotes, and identifying them requires a thorough understanding of the function’s properties.
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