Method: Continuity Using a Graph

Step 1: Identify all the x-values where you would have to lift your pencil in order to draw the given graph. These are usually going to be found at holes in the graph, vertical asymptotes, and jumps.

Step 2 (Optional): Show why those x-values are not continuous. You will not always be asked to show why those x-values are not continuous, but you sometimes are. Which means you must be able to determine what part of the definition of a continuous function, $\underset{x\to c}{\lim }\mathit{ }\mathit{f}\mathit{\left(}\mathit{x}\mathit{\right)}\mathit{=}\mathit{f}\mathit{\left(}\mathit{c}\mathit{\right)}$,your x-value does not agree with using the graph.