How Do You Find Vertical & Horizontal Asymptotes?
Some functions are continuous from negative infinity to positive infinity, but some break off at a point of discontinuity or turn off and never make it past a certain point. An asymptote is either a straight or curved line that defines the value the function a function approaches if it does not extend to infinity in opposite directions. Horizontal and vertical asymptotes are the easiest to find, but each one requires a slightly different method. Write the function for which you are trying to find a vertical asymptote. These most likely will be rational functions, with the variable x somewhere in the denominator. When the denominator of a rational function approaches zero, it has a vertical asymptote. Find the value of x that makes the denominator equal to zero. If your function is y = 1/(x+2), you would solve the equation x+2 = 0, which is x = -2. There may be more than one possible solution for more complex functions. Take the limit of the function as x approaches the value you found
