Limits and Continuity

Lesson 6

Objective

Write and evaluate piecewise functions algebraically and graphically using parent functions.

Criteria for Success

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  1. Know the structure and domain of 12 parent functions.
  2. Match domains of a piecewise graph with an appropriate parent function.
  3. Write piecewise functions using transformations of parent functions.
  4. Evaluate limits of nonlinear piecewise functions.
  5. Describe continuity of nonlinear piecewise functions.

Tips for Teachers

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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, EK1.2A2 (approaching)

Anchor Problems

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Problem 1

Draw a sketch of each of the parent functions shown in the table below.

Parent functions:

$${\mathrm{ln}(x)}$$ $${e^x}$$ $${x^2}$$ $${x^3}$$ $${|x|}$$

$$c$$

(where $$c$$ is a constant)

$${\sqrt{x}}$$ $${\sqrt[3]{x}}$$ $${\mathrm{sin}(x)}$$ $$\mathrm{cos}(x)$$ $${1\over x}$$ $$x$$

Guiding Questions

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Problem 2

Write the piecewise function for the graph shown below.

Guiding Questions

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Problem Set

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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.

  • Given the graph of a piecewise function, write the function algebraically with domain restrictions. Don’t need to do any more than two pieces
  • Given the equations of a piecewise function, draw the graph. Don’t need to do any more than two pieces
  • Practice other parts of the unit as necessary within the questions of the problem set
  • Adapt questions to focus on parent functions that students need additional practice with
  • Emphasize interval notation on infinite domains (for instance, $${(3, \infty)}$$) in this lesson 

Target Task

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Write a function for the graph shown below.