Continuous function

Intuitively, a continuous function is a function that we can draw with only one line. Otherwise, a function is said to be "discontinuous“.

Examples:

I is continuous in R-{-1,2}

II is continuous in R-{2}

III is continuous in [-2,1)U(1,4]

IV is continuous in [-4,-2)U(-2,0)U(0,4]

Exercise: study where these functions are continuous:

a)

b)

Solutions: a) f is continuous in R-{1}; b) f is continuous in R-Z