Limits and Continuity

1. Define continuity of a function $$f$$ at a point $$a$$ as $$f(a)$$ exists, $$\lim_{x\rightarrow a}f(x)$$ exists, and $$\lim_{x\rightarrow a}f(x)=f(a)$$.
2. Determine whether a function meets the criteria for continuity on a particular domain.
3. Determine intervals on which a function is continuous.
4. Sketch functions given constraints on continuity.

The definition of continuity used in Anchor Problem #1 is a common definition, but the target task uses an alternate definition. Students should build an intuitive understanding of continuity and understand that there are multiple formal ways to describe this idea.

Below are four conditions. If a point $$a$$ on a function $$f$$ meet these conditions, is it continuous?

A:  $$\lim_{x\rightarrow a^+}f(x)$$ exists

B:  $$\lim_{x\rightarrow a^-}f(x)$$ exists

C:  $$f(a)$$ exists

D:  $$\lim_{x\rightarrow a^+}f(x)=\lim_{x\rightarrow a^-}f(x)=f(a)$$