Asymptote

Definition of Asymptote

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

Examples of Asymptote

Solved Example on Asymptote

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).

Related Terms for Asymptote

• Line
• Graph

Additional Links for Asymptote

• Click here for samples
• Back to Mathematics Dictionary