To decide whether lim_x→a  f(x) exists, and to find its value if it does:

Step 1. Draw the graph of f(x) either by hand or using technology, such as a graphing calculator.
Step 2. Position your pencil point (or the graphing calculator "trace" cursor) on a point of the graph to the right of x = a. In the example illustrated, we are estimating limx→-2 f(x), so we have a = -2. Therefore, we position our trace point on the graph to the right of x = -2.
Step 3. Move the point along the graph toward x = a from the right and read the y-coordinate as you go. The value the y-coordinate approaches (if any) is then the limit  lim xa f(x). In the example we are doing, notice that the y-coordinate is approaching 2 as x approaches -2 from the right. (See the moving graphic on the right. If it has vanished, click on the graphic icon to reload it.) Therefore,   lim x-2 f(x) = 2.
Step 4. Repeat Steps 2 and 3, but this time starting from a point on the graph to the left of x = a, and approach x = a along the graph from the left. The value the y-coordinate approaches (if any) is then  lim xa f(x). In the example we are doing, the y-coordinate is again approaching 2 as x approaches -2 from the left. Therefore,   lim x-2 f(x) = 2.
Step 5. If the left and right limits both exist and have the same value L, then lim xa f(x) exists and equals L. In our example, the left and right limits both exist and equal 2, and so  lim xa f(x) = 2.