When we say a function has a point of continutity?
We say a function has a point of continuity if “the limit from negative infinity to the point in concern” is the same VALUE as ” the limit from positive infinity to the point in concern”.
Follow this idea and note that “positive infinity” and “negative infinity” may be equivalently replaced by “upper bound” and “lower bound” respectively if the function is defined on a “limited range of values!”.
Just do the ‘limits’ from both ends and if the value is same, we say the function has a point of continuity at that point. If its true for ‘all points’ in that function, we can then say that the function is continuous.