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Please Note!
The purpose of Algebra Answers is to help students in an efficient manner with algebra. Hiring a tutor can be costly and time consuming so it is the intent of Algebra Answers to provide a more efficient algebra help service than typical tutoring. It is not the intent of Algebra Answers to help any student or students cheat on homework or tests. The sole intent is to help students obtain a greater understanding of algebra by seeing difficult problems worked out to completion.
Asymptote

Asymptotes are formally defined using limits. The graph of the function approaches a value but will never reach it.

An example of asymptotes can be seen in the image below of the equation y = 1/x, in which two asymptotes are seen: the horizontal line y = 0 and the vertical line x = 0. In this example as the equation approaches the y-axis it will get increasingly small but will never reach zero. Think of the largest value you can and plug it in. 1 divided by your number will never reach zero.

On the other side, no matter how small of a number you plug in it will grow and grow and grow without an upper bounds. In each case the function approaches infinity as it apporaches the axis.