Use the definitions and intuitive meanings of the terms and processes:

...|f(c) - 0| < (some small value).

Is "limit exists at" the same thing as "continuous at"?

What is the definition of "continuous"?

Suppose that fiscontinuous at c, so that lim, x->c, f(x) = f(c). What does this tell you about g(c)?

Take a close look at the definitions and theorems. Does this half-open interval fulfill the requirements for this conclusion?

Think about a rational function you've graphed recently, like in your algebra class. Did you draw infinitely-many vertical asymptotes?

Think about the trig functions you've graphed. What do a couple of them look like, with respect to vertical asymptotes?