a basic way to know if a function is continuous is to use a pencil or your finger. then, start at the left of the function. then, move your finger along the path of the function. if you ever need to lift your finger or pencil to keep following the function, then you know it is not continuous. this is because, by lifting your finger, you have "jumped" from one section of the function to another. that means you made a very small movement but the function changed very much. this is what the first sentence of this article is talking about.