CK-12-Pre-Calculus Concepts

http://www.ck12.org Chapter 1. Functions and Graphs

2. Describe the discontinuities of the function below.


3. Describe the discontinuities of the function below.

Answers:

1. The function seems to oscillate infinitely asxapproaches zero. One thing that the graph fails to show is that 0 is
   clearly not in the domain. The graph does not shoot to infinity, nor does it have a simple hole or jump discontinuity.
   Calculus and Real Analysis are required to state more precisely what is going on.


2. There is a jump discontinuity atx=−1 and an infinite discontinuity atx=2.


3. There are jump discontinuities atx=−2 andx=4. There is a removable discontinuity atx=2. There is an
   infinite discontinuity atx=0.

Practice

Describe any discontinuities in the functions below:
1.y=x