• Definition of “continuity” in everyday language
A function is continuous
if it has no holes, asymptotes, or breaks
. A continuous
graph can be drawn without removing your pen from the paper.
• Definition of “continuity” in Calculus
is continuous at a number a
• Polynomials are always continuous everywhere.
Rational functions are continuous wherever the functions are defined; in other words, avoiding holes and asymptotes, rational functions are continuous everywhere.
A function f is continuous at a number a, if and only if:
In simple words, the graph of a continuous function has no break in it and can be drawn without lifting your pen from the paper.