Curriculum / Math / 11th Grade / Unit 9: Limits and Continuity / Lesson 5
Math
Unit 9
11th Grade
Lesson 5 of 9
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Lesson Notes
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Define continuity of functions and determine whether a function is continuous on a particular domain.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
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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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
25-30 minutes
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?
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
5-10 minutes
Below are four conditions. If a point $$a$$ on a function $$f$$ meet these conditions, is it continuous?
A:Â Â $$\lim_{x\rightarrow a^+}f(x)$$Â exists
B:Â Â $$\lim_{x\rightarrow a^-}f(x)$$Â exists
C:Â Â $$f(a)$$Â exists
D:Â Â $$\lim_{x\rightarrow a^+}f(x)=\lim_{x\rightarrow a^-}f(x)=f(a)$$
Next
Write and evaluate piecewise functions algebraically and graphically using parent functions.
Topic A: Limits and Continuity
Graph, write, and evaluate linear piecewise functions.
Use interval and function notation to describe the behavior of piecewise functions.
Sketch a slope graph from a linear piecewise function.
Find limits, including left- and right-hand limits, on a function given graphically.
State and evaluate limits algebraically.
Evaluate infinite limits and limits at infinity.
Sketch functions given limits and continuity requirements.
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