Method: Finding Limits of a Graph

Here is the method that I follow when solving a limit problem given a graph.

Step 1: Draw a “wall” at the $a–\mathit{value}$ ($x–\mathit{value}$) you are heading towards.

Step 2: Determine what type of limit you are being asked to evaluate.

–          LHL ($–$)

–          RHL ($+$)

–          Overall

Step 3: Draw along your graph starting from the side (left or right) or both sides (overall) based upon what you determined in Step 2. Continue along your graph until you run into the “wall” you drew in Step 1.

The $y–\mathit{value}$where you run into the “wall” is the answer to your limit question. Remember that limits do not care if there is an actual value there (dot on the graph) or no value (open circle). They only care what does it look like I am heading towards? Where would I run into the wall?