3. continuous function

A continuous function is a function for which, intuitively, "small" changes in the input result in "small" changes in the output. Otherwise, a function is said to be "discontinuous“.

Examples:

- f, g are continuous in R
- p is continuous in its domain    dom p= R-{3}
- q is continuous in R- {3}

 

Exercise: study the continuity of these functions:

a) 

b) 

c) 

 

 

Solutions: a) (-∞,2)U(2,6); b) R; c) (-1,2)U(3,5)U(5,8)