Curriculum / Math / 11th Grade / Unit 9: Limits and Continuity / Lesson 9
Math
Unit 9
11th Grade
Lesson 9 of 9
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Lesson Notes
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Sketch functions given limits and continuity requirements.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
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This lesson is aligned to the Learning Objectives and Essential Knowledge described in the College Board's AP Calculus AB and AP Calculus BC Course and Exam Description:
LO1.1A(b): EK1.1A1, EK1.1A2, EK1.1A3
LO1.1B: EK1.1B1
LO1.2A: EK1.2A1
Note: This lesson will also serve as the review for this unit.
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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
For the function $${f(x)}$$, given below, determine the following:
Let $${f(x)}=\begin{Bmatrix} x^2-5 & x\leq 3 \\ x+2 & x>3 \end{Bmatrix}$$
Write your answers in limit notation.
Draw a picture of a function with the following properties:
$${\lim_{x\rightarrow a^+}f(x)\neq \lim_{x\rightarrow a^-}f(x)}$$
$${\lim_{x\rightarrow a^+}f(x) = f(a)}$$
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
5-10 minutes
Draw the picture of a function where $${f(c)=\lim_{x\rightarrow c^+}f(x)}$$, but the limit at $${x=c}$$ does not exist.
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.
Define continuity of functions and determine whether a function is continuous on a particular domain.
Write and evaluate piecewise functions algebraically and graphically using parent functions.
State and evaluate limits algebraically.
Evaluate infinite limits and limits at infinity.
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