Use the graph to determine the following limits,and discuss the continuity of the function at . (i) (ii) (iii)

Question

Use the graph to determine the following limits,and discuss the continuity of the function at  . (i)  (ii)  (iii)  ​

Quizplus · Accepted Answer

(i) To find the limit as x approaches -2 from the right, we need to look at the graph to see where the function approaches. As x approaches -2 from the right, the function approaches 0. Therefore, the limit is 0.
(ii) To find the limit as x approaches -2 from the left, we need to look at the graph to see where the function approaches. As x approaches -2 from the left, the function approaches 1. Therefore, the limit is 1.
(iii) To find the limit as x approaches -2, we need to look at the graph to see if the left and right limits exist and are equal. However, as we can see from the graph, the left and right limits do not exist because the function approaches different values as x approaches -2 from the left and right. Therefore, the limit as x approaches -2 does not exist.
Since the limit as x approaches -2 does not exist, the function is not continuous at x = -2. Therefore, options A, B, and D can be eliminated. 
From the graph, we can see that the function approaches 0 as x approaches 0 from the right and approaches 1 as x approaches 0 from the left. Therefore, the limit as x approaches 0 exists but is not equal on both sides. This means that the function is not continuous at x = 0. 
Thus, the correct answer is C: 0, 1, does not exist, not continuous.

Use the Graph to Determine the Following Limits,and Discuss the Continuity