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.
>>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.