Functions and Transformations

Lesson 2

Math

Unit 5

9th Grade

Lesson 2 of 16

Objective


Graph piecewise functions presented algebraically and write piecewise functions from graphs.

Common Core Standards


Core Standards

  • F.IF.A.2 — Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
  • F.IF.B.4 — For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Modeling is best interpreted not as a collection of isolated topics but in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appear throughout the high school standards indicated by a star symbol (★). The star symbol sometimes appears on the heading for a group of standards; in that case, it should be understood to apply to all standards in that group.
  • F.IF.C.7.B — Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.

Foundational Standards

  • 8.EE.B.5
  • 8.EE.B.6
  • 8.F.B.4

Criteria for Success


  1. Understand a piecewise function as a function whose domain is divided into multiple intervals, each defined by a different function rule that represents the changes in behavior.
  2. Graph piecewise functions written algebraically in function notation.
  3. Write piecewise functions, in function notation, from graphs.
  4. Describe features of piecewise functions including boundary lines, rates of change, and domain and range.
  5. Describe how a function would change if the domain or range were altered, in situations with and without context.
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Anchor Problems


Problem 1

A piecewise function is shown below.

Describe:

  1. where the graph changes behavior
  2. the domain that represents each behavior of the graph
  3. the different rates of change
  4. what happens at $${ x=1}$$
  5. how the graph would change if $${ f(x)=3}$$ for $${-3≤x≤1}$$

Guiding Questions

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Problem 2

Graph the following piecewise function.

  

Guiding Questions

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Problem 3

Write a piecewise function to represent the graph below. Use function notation.

Guiding Questions

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Problem Set


Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.

Target Task


Graph the piecewise function 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.

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Lesson 1

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Lesson 3

Lesson Map

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

Topic A: Piecewise Functions

Topic B: Absolute Value Functions

Topic C: Function Transformations

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