Curriculum  /  Math  /  11th Grade  /  Unit 9: Limits and Continuity  /  Lesson 6

Limits and Continuity

Lesson 6

Math

Unit 9

11th Grade

Lesson 6 of 9

Objective

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

Criteria for Success

  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

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)

Fishtank Plus

Unlock features to optimize your prep time, plan engaging lessons, and monitor student progress.

Anchor Problems

25-30 minutes

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

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

Problem 2

Write the piecewise function for the graph shown below.

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

Target Task

5-10 minutes

Write a function for the graph shown below.

Additional Practice

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.

  • 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 

Next

State and evaluate limits algebraically.

Lesson 7
icon/arrow/right/large

Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Limits and Continuity

Request a Demo

See all of the features of Fishtank in action and begin the conversation about adoption.

Learn more about Fishtank Learning School Adoption.

Contact Information

School Information

What courses are you interested in?

ELA

Math

Are you interested in onboarding professional learning for your teachers and instructional leaders?

Yes

No

Any other information you would like to provide about your school?

We Handle Materials So You Can Focus on Students

We Handle Materials So You Can Focus on Students

We've got you covered with rigorous, relevant, and adaptable math lesson plans for free