Continuous function
English: A functin from R to R is continuous iff, informally, its value changes only slightly when its input changes slightly.
Examples
A continuous function
A function discontinuous at one point, yet right-continuous there
Counterexamples (discontinuous functions)
jump discontinuity
- A function discontinuous at one point, yet right-continuous there
A function discontinuous at one point, yet left-continuous there
A function discontinuous at one point
Function discontinuous at both points
A function discontinuous at several points
Removable discontinuity
A function that has a removable discontinuity at x0 with a point underneath
Continuous from the right with nothing on the left
Square root of x graph. Continuous only from 0 through the right. No points before 0.
Xth root of x graph
.PNG)
infinite discontinuity
Tangent of x has an infinite discontinuity at pi/2,-pi/2,3pi/2 and so on - infinite amount of infinite discontinuities
1/x graph 1 infinite discontinuity
Rational function with two infinite discontinuities
=1÷x_20211118.svg)
functions with a finite domain
Inverse sine function graph, y=arcsin(x) , the graph has x values from (-1,1)
