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
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).