Curriculum / Math / 11th Grade / Unit 9: Limits and Continuity / Lesson 1
Math
Unit 9
11th Grade
Lesson 1 of 9
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Graph, write, and evaluate linear piecewise functions.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
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Desmos has a tutorial, Learn Desmos: Restrictions, on creating graphs with domain or range restrictions. Take a look at this before creating the problem set and note that open and closed points must be added separately from the functions.
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
Write the piecewise function shown in the graph below.
Graph the following piecewise function. Describe whether the function is continuous or discontinuous.
$$f(x)=\left\{\begin{matrix} -{1\over2}x+4, \space x>2 \\ -2x+1, \space \space \space -2<x\leq2 \end{matrix}\right.$$
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
Graph the piecewise function.
$${f(x)=\left\{\begin{matrix}x-4, \space \mathrm{if}\space x\leq1 \\ 3x,\space \mathrm{if}\space x>1 \end{matrix}\right.}$$
Write equations for the piecewise function shown below.
The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.
Lesson 2
Topic A: Limits and Continuity
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.
Sketch functions given limits and continuity requirements.
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