CK-12-Pre-Calculus Concepts

1.9. Asymptotes and End Behavior http://www.ck12.org

Answers:

1. There is a vertical asymptote atx=0. Asxgets infinitely small, there is a horizontal asymptote aty=−1. Asx
   gets infinitely large, there is another horizontal asymptote aty=1.


2. There is a vertical asymptote atx=2. Asxgets infinitely small there is a horizontal asymptote aty=−1. Asx
   gets infinitely large, there is a horizontal asymptote aty=1.


3. There is a horizontal asymptote aty=−1 asxgets infinitely small. This is becauseeraised to the power of a
   very small number becomes 0.000000... and basically becomes zero.

Practice

Identify the asymptotes and end behavior of the following functions.
1.y=x

2.y=x^2

3.y=x^3