Question

Which of the following functions are continuous. Select all that apply.

Answer 1

Answer:

The function which are continuous are:

                Function 2 and Function 3.  (graphs attached)

Step-by-step explanation:

We know that a function is said to be a continuous function if the limit at each of the points exist and is equal to the value of the function at that point.

Also, in the graph of a continuous function there is no break i.e. the graph is connected at all the points.

• Here we observe that in the first graph there is a break close to x=0.

      and hence the function is not continuous.

• The graph of second function is continuous since the limit exist at all the points.

• The graph of the third function is again continuous.

• But the graph of the fourth function is not continuous since, the left as well as right hand limit at  x= -1 is not equal.

This means that the limit at x= -1 does not exist and hence the function is not continuous.

Answer 2

>>1st one- at X=0 Y=DNE so the function is not continious.
>>2nd one- there is Y value for every X so the function is continious.
>>3rd one- there is Y value for every X so the function is continious.
>>4th one- f(-1)=1 does not equal the limit of f(x).


because the limit as X aprroaches from the left and from ther right is different.