Also, as x obtain very large, both positive & negative, the graph approaches the line specified by y = 0 . This line is called a horizontal asymptote.
Following are the general definitions of the two asymptotes.
1. The line x = a is vertical asymptote if the graph rise or fall without bound on one or both sides of the line as x moves in closer & closer to x = a .
2. The line y = b is horizontal asymptote if the graph approaches y = b as x increases or decreases without bound. Note that it doesn't have to approach y = b as x BOTH increases and decreases. Only it needs to approach it on one side in order for it to be a horizontal asymptote.
Determining asymptotes is in fact a fairly simple procedure. First, let's begin with the rational function,
where n refer to the largest exponent in the numerator and m refer to the largest exponent in the denominator.
Then we have the given facts regarding asymptotes.
1. The graph will have vertical asymptote at x = a if the value of denominator is zero at x = a and the numerator isn't zero at x = a .
2. If n < m then the x-axis is the horizontal asymptote.
3. If n = m then the line y = a/ b is the horizontal asymptote.
4. If n > m there will be no horizontal asymptotes.
The procedure for graphing a rational function is somewhat simple. Following it is.