Asymptotes
If a function f gets close to a certain number L when x gets larger and larger, then we say that the limit as x goes to infinity is L and we write:
If a function An important result: If Inclined asymptotes have an equation y = kx + q and their position is arbitrary except vertical. In order a straight line y = kx + q be an asymptote, the coefficients k and q must satisfy at least one pair of the following conditions
Naturally these limits must be finite real numbers. A certain function can have maximally two inclined asymptotes.
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. Likewise, if f gets close to L when x gets smaller and smaller, then the limit as x goes to negative infinity is L and we write: 
. In both cases, the line y = L is a horizontal asymptote of f.
Example: 
because when x is very large, 
is close to 0. The x -axis is a horizontal asymptote of the function 
:
gets larger and larger as x gets close to a number a, then it “goes to infinity” and we write: 
. The line x = a is a vertical asymptote of f. Similarly, if 
. Again, the line x = a is a vertical asymptote of f.
then 
. This is because one over a very large positive number and one over a huge negative number are both close to 0.
and 
(k and b are numbers).
