Continuity Under Composition of Functions-2

Compare graph of function f in window 1 with graph of the function in window 2 obtained by composing f with natural log function in terms of continuity. Remember that natural log function is a continuous function. Click on Next Example button to generate more examples. Conjecture based on your exploration.
For more on limit and continuity of a function check my online book "Flipped Classroom Calculus of Single Variable"