# Difference between revisions of "Math 22 Continuity"

Jump to navigation
Jump to search

(→Notes) |
|||

Line 13: | Line 13: | ||

==Notes== | ==Notes== | ||

− | Polynomial function is continuous on the entire real number line (ex: <math>f(x)=2x^2-1</math> is continuous on <math>(-\infty,\infty)</math>) | + | ''Polynomial function'' is continuous on the entire real number line (ex: <math>f(x)=2x^2-1</math> is continuous on <math>(-\infty,\infty)</math>) |

+ | ''Rational Functions'' is continuous at every number in its domain. (ex: <math>f(x)=\frac {x+2}{x^2-1}</math> is continuous on <math>(-\infty,-1)\cup (-1,1)\cup (1,\infty)</math>) | ||

'''This page were made by [[Contributors|Tri Phan]]''' | '''This page were made by [[Contributors|Tri Phan]]''' |

## Revision as of 08:05, 16 July 2020

## Continuity

Informally, a function is continuous at means that there is no interruption in the graph of at .

## Definition of Continuity

Let be a real number in the interval , and let be a function whose domain contains the interval . The function is continuous at when these conditions are true. 1. is defined. 2. exists. 3. If is continuous at every point in the interval , then is continuous on theopen interval.

## Notes

*Polynomial function* is continuous on the entire real number line (ex: is continuous on )
*Rational Functions* is continuous at every number in its domain. (ex: is continuous on )

**This page were made by Tri Phan**