Define continuity of functions and determine whether a function is continuous on a particular domain.
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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.
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The conditions under which a function $$f$$ is "continuous" at a point $$a$$ are:
A: $$f(a)$$ exists
B: $$\lim_{x\rightarrow a}f(x)$$ exists
C: $$\lim_{x\rightarrow a}f(x) = f(a)$$
The graph below shows $${{f(x)}=|x|}$$. Sketch a slope graph of $${f(x)}$$.
On what interval(s) is the slope graph continuous? What features of a function cause its slope graph to be discontinuous?
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The following resources include problems and activities aligned to the objective of the lesson that can be used to create your own problem set.
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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: $$\lim_{x\rightarrow a^+}f(x)=\lim_{x\rightarrow a^-}f(x)=f(a)$$