Use the given graph to determine the limit, if it exists. A coordinate graph is shown with a horizontal line crossing the y axis at four that ends at the open point 2, 4, a closed point at 2, 1, and another horizontal line starting at the open point 2, -1. Find limit as x approaches two from the left of f of x. and limit as x approaches two from the right of f of x.. 1; 1 -1; 4 4; -1 Does not exist; does not exist

Well, in case you want to know why it is right, here goes:

If you are approaching 2 from the left you would be looking at the graph for values of x<2. So you would be "traveling" on that straight, horizontal line that crosses the y-axis at 4. The line y=4. Even though the graph at x=2 does not equal 4, if you are coming at it from the left you are walking along the line and approaching 4. The limit is 4.

If you are approaching 2 from the right you look at values of x greater than 2. x>2. Here you are traveling on the horizontal line that if extended would cross the y-axis at -1. That is, the line y=-1. So even though the value of the function at x=2 is not -1, if you walk along this line from right to left you are indeed approaching a y value of -1. The limit is -1.

If it is of interest, since the limit from the left and right are not equal and not equal to F(2)=1, the limit as x approaches 2 does not exist. That is, the left-hand (from the left) and right hand (from the right) limits exist but the limit itself (two sided limit) does not. You were not asked this but it is a very common follow-up question given what you were asked.