Definition Of Asymptote

Asymptote is a line that a graph gets closer and closer to, but never touches or crosses it.

Examples of Asymptote

Video Examples: Asymptotes of Rational Functions

Solved Example on Asymptote

Ques: Find the vertical asymptote of the graph of the function  .

Choices:

A. x = - 1
B. x = 1
C. x = 0
D. x = 2
Correct Answer: B

Solution:

Step 1: is clearly discontinuous at x = 1.
Step 2: If then the line x = c, is the vertical asymptote. [Definition.]
Step 3:  [For the vertical asymptote.]
Step 4:  [Numerator is positive, denominator is a very small positive number.]
Step 5:  [For the vertical asymptote.]
Step 6: [Numerator is positive, denominator is a very small negative number.]
Step 7: So, x = 1 is the vertical asymptote of the curve f (x).

 

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