1. Asymptotes Of Other Rational Functions Functions By the end of this lesson you will be able to explain/calculate the following: 1.Vertical Asymptotes 2.Horizontal Asymptotes

2. Asymptotes Of Other Rational Functions asymptote is a line  An asymptote of a curve is a line such that the distance between the curve and the line approaches zero as they tend to infinity asymptotos  The word asymptote is derived from the Greek asymptotos which means "not falling together“  For curves given by the graph of a function y = ƒ(x), there are potentially three kinds of asymptotes: 1. horizontal, 2. vertical, and, 3. oblique asymptotes

3. Vertical Asymptotes  The function f(x) =has the graph given below.  Notice that at x = 1, f(x) is undefined. vertical asymptote  Since the graph approaches the vertical line x = 1, we say that x = 1 is a vertical asymptote.  We can write:  as x  1 (from the left), f(x)  –   as x  1 (from the right), f(x)   or alternatively,  as x  1–, f(x)  –   as x  1+, f(x)  

4. Horizontal Asymptote horizontal asymptote  This indicates that y = 2 is a horizontal asymptote and we write:  as x  , y  2  as x  – , y  2  or alternatively,  as x  , y  2+  as x  – , y  2–

5. Exercise 1G