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This is a great instructional video on how to find oblique asymptotes of rational functions. If you believe that your own copyrighted content is on our Site without your permission, please follow this Copyright Infringement Notice procedure. Before we come to the definition of a vertical asymptote, let us first see what an asymptote is:An asymptote is a line with respect to a curve such that the curve approaches that line, but does not touch it even if both the line and the curve are extended infinitely.
A vertical asymptote essentially refers to the value of x at which the function f(x) approaches infinity. Let us look at the following examples to actually see how vertical asymptotes can be found. We know from our unit circle that cos(x) is zero when x = $\frac{pi}{2}$ and $\frac{3pi}{2}$.

We can also say that the value of x at which the function f(x) is not defined or does not exist. We simply set the denominator equal to zero and the values of x at which the denominator equals zero are the vertical asymptotes. Basically asymptote of a curve is a line such that the distance between the line and the curve approaches 0 (zero) as they tend to $\infty$ (infinity).
This is simply because in a rational function the function would not exist for the values of x that make the denominators equal to zero.For trigonometric functions, we need to find the points on the x axis where the value of the function is infinity or does not exist. The higher power here is x square which is at the top and hence we have to find oblique asymptotes of this function.When we divide x square+4x-12 by x-6 we get x=10 and the reminder is 48. We shall see how exactly this is done in the next section where we will solve sample problems.

As name suggested, vertical asymptote is a vertical line near which the function expand without bound and horizontal asymptote is a horizontal line that the function graph approaches as independent function varies between ($- \infty, \infty$). Thus the equation of a vertical asymptote would be of the form:VA=x=aWhere, a = the point on the x axis where the function is not defined. Step 2 :Clearly, the exponent of the numerator is greater than the exponent of the denominator by one.

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