Given the graph of in the figure, determine all x-values from F, G, H, or I for which the function is continuous.
A)G H
B)G H I
C)F G H I
D)F G

Question

Given the graph of  in the figure, determine all x-values from F, G, H, or I for which the function is continuous. ​  ​
A)G H 
B)G H I 
C)F G H I 
D)F G

Quizplus · Accepted Answer

The function is continuous at a point if the limit exists and is equal to the function value at that point. From the graph, we can see that the function is continuous at G, H, and I because there are no jumps or holes at these points. The function is not continuous at F because there is a jump discontinuity. Therefore, the choices that include G, H, and I (B, C, and E) are all possible answers. However, choice C includes F, which is not continuous, so it is not the best choice. Therefore, the best choice is B.

Given the Graph of in the Figure, Determine All