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## Homework Statement

so a function was only continuous if and only if lim x ---> a = f(a)

but I read some other books saying a functions continuity can only be judged based on their allowed domains. Does that mean the first definition fails if the domains of where the rule fails are explicitly stated or when using a "familiar" parent graph?

## Homework Equations

refer to above

## The Attempt at a Solution

the book I read,the humongus of calculus, said but I read some other books saying a functions continuity can only be judged based on their allowed domains. The book doesn`t seem to serious with math. I don`t know how to approach this. I think the book meant to say that this only applies to continuity over an interval rather than the meaning a whole function was continuous.