Linear Functions and Applications

Lesson 13

Math

Unit 1

11th Grade

Lesson 13 of 13

Objective


Write piecewise functions from contextual situations.

Common Core Standards


Core Standards

  • A.CED.A.2 — Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
  • A.CED.A.3 — Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.
  • 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

  • A.CED.A.1
  • F.IF.B.4
  • F.IF.C.9

Criteria for Success


  1. Define the variables of a piecewise function in a contextual situation. 
  2. Use information about whether the rate of change of a situation is increasing, decreasing, or zero, and key points of change from a contextual situation to write the piecewise function. 
  3. Describe how the function that is described in context may need to be adjusted for the domain restriction algebraically. 
  4. Write, graph, and evaluate contexts represented by step functions.
Fishtank Plus

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

Anchor Problems

25-30 minutes


Problem 1

Below is a piecewise function that relates yards traveled and seconds. 

Write a story that would result in this graph to model the situation.

Guiding Questions

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

Problem 2

Your favorite dog groomer charges according to your dog’s weight. If your dog is 15 pounds and under, the groomer charges $35. If your dog is between 15 and 40 pounds, she charges $40. If your dog is over 40 pounds, she charges $40, plus an additional $2 for each pound. 

  1. Write a piecewise function that describes what your dog groomer charges. 
  2. Graph the function. 

Guiding Questions

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

Target Task

5-10 minutes


Your summer job pays you $8 for the first 20 hours you work and then time and a half for the next 10 hours you work. If you work more than 30 hours, you do not get paid any more. 

  • Write a piecewise function that models your summer pay possibilities. 
  • Graph your piecewise function. 

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.

  • Include a problem where students need to write the piecewise function for Anchor Problem #1. 

Lesson Map

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

Topic A: Features of Linear Functions

Topic B: Systems of Functions and Constraints

Topic C: Piecewise Functions

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