Question

Is my answer correct?

Answer 1

The answer is actually the last choice.

A function does not need to make sharp turns in order to be continuous.

For example, `f(x) =x` is continuous for every point in its domain; however, there are no sharp turns anywhere in a line.

Your answer is incorrect: the limit of the function must exist as `x->a`. If you said the third choice was correct, then the second choice must also be correct. Since the limit of the function as `x->a` is equal to the value of the function at `x=a`, the limit must exist. In other words, if `lim_(x->a) f(x) = f(a)`, then `lim_(x->a) f(x)` exists.