Continuous Function?

>>310138
An easy way to test for continuity is if you can differentiate it.

Basically, if you have a graph, if there are no breaks and no corners (look up y=|x|, that is not continuous) it is continuous

>>310140
This guy is not correct, a function does not need to be differentiable to be continuous.

Read this:
http://www.intmath.com/functions-and-graphs/7-continuous-discontinuous-functions.php

For example the image you posted is a continuous function.

This image is not:
http://math-faq.com/wp/wp-content/uploads/2014/09/10_5_1_5.jpg

>>310138
Following up an easy way to tell if a function is continuous is to do this:

Can you draw the graph of that function without ever once lifting your pencil? If the answer is yes, then it is continuous, if not it is discontinuous.

>>310138
a function is continuos if the limit when the function tends to an arbitrary value diferent from infinity always exist, basically if the curve doesn't have holes, where the function is not defined, and if it doesn't have points where the curve breaks, or asymptotes

continuity basically means that for every value you plug into x that you get a real value for y, and that the function is defined everywhere on its range.

you can find continuity from what >>310141
said, but he got it backwards

all differentiable functions are continuous, so you can differentiate the function, and if its defined then its continuous! However, not all continuous functions are differentiable. again >>310141 is wrong here, as the absolute value function IS continuous, but is not differentiable everywhere

essentially so long as there are not holes or breaks, no odd jumps or places where the graph of the function gets snipped then you're good.

you can find discontinuities through graphing, or if you only have the function and it seems hard to graph, then look for places where radicals would be negative, denominators valued at zero, and if you are given a set of functions, test the end points. its that easy