How do you determine if a graph is asymptotic? - Answers

A graph of y against x has an asymptote if, its y value approaches some value k but never actually attains it. The value k is called its asymptotic value. These are often "infinities" when a denominator in the function approaches 0. For example, y = 1/(x-2) has an asymptotic value of minus infinity when x approaches 2 from below and an asymptotic value of + infinity from above. But the asymptotic value need not be infinite - they could be a "normal number. For example y = 3-x + 2.5 has an asymptotic value of 2.5. y is always greater than 2.5 and as x increases, it comes closer and closer to 2.5 but never actually attains that value.