Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false.
The function is continuous on .

A) The function is continuous and nonzero on , then the function is continuous in , so the statement is true.
B) The function is continuous but zero when , then the function is not continuous in , so the statement is false.

Question

Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. ​
The function  is continuous on  .
​
A) The function is continuous and nonzero on , then the function is continuous in , so the statement is true. 
B) The function is continuous but zero when , then the function is not continuous in , so the statement is false.

Quizplus · Accepted Answer

This statement is true by the intermediate value theorem. Since the function is nonzero and continuous on the interval 11eb651f_cb40_440f_b0a1_ad3c75a5807a_TB8255_11, it must take on all values between its minimum and maximum values on that interval. Therefore, it must also be continuous on the interval 11eb651f_cb40_4411_b0a1_4dfc6fd23bb3_TB8255_11.

Determine Whether the Statement Is True or False