Curriculum  /  Math  /  9th Grade  /  Unit 5: Functions and Transformations  /  Lesson 11

Functions and Transformations

Lesson 11

Math

Unit 5

9th Grade

Lesson 11 of 16

Objective

Identify solutions to a system of absolute value and linear functions graphically and algebraically.

Common Core Standards

Core Standards

  • A.REI.A.1 — Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
  • A.REI.C.6 — Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
  • A.REI.D.11 — Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. 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.

Foundational Standards

  • 8.EE.C.7
  • 8.EE.C.8

Criteria for Success

  1. Describe that two sides of the equals or inequality sign can be represented as two functions, equal or compared to one another, as in $${ f(x)=g(x)}$$ or $${ f(x)>g(x)}$$.
  2. Describe how the process of finding the solutions to an absolute value equation or inequality is the same, even when there are variables in the non-absolute value function. 
  3. Find the solution(s) to a system of absolute value and linear functions, and identify extraneous solutions.
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Anchor Problems

25-30 minutes

Problem 1

Functions $${f(x) }$$ and $${g(x)}$$ form a system of equations. Let $${f(x)=|x+2|-3}$$ and $${g(x)}=0.5x+1$$. 

When is $$f(x)>{g(x)}$$? Find the solution(s) to the system algebraically and graphically (may use technology).

Guiding Questions

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References

EngageNY Mathematics Algebra I > Module 3 > Topic C > Lesson 16 — Opening Exercise 1-2

Algebra I > Module 3 > Topic C > Lesson 16 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by Fishtank Learning, Inc.

Problem 2

Function $${ f(x)}$$ is shown below.

$${f(x)=|x-1|}$$

Find a function $${g(x)}$$ such that the system has:

  1. two solutions
  2. one solution
  3. no solutions

Guiding Questions

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Problem Set

15-20 minutes

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

Target Task

5-10 minutes

Find the solution to this system algebraically and graphically. 

$${f(x)=|x+2|-1}$$
$${g(x)={1\over2}x+3 }$$

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 mix of problems, similar to the Anchor Problems and Target Task, that are equations and inequalities. Ensure students check for extraneous solutions by either substituting or graphing.

Next

Identify and describe vertical translations of functions.

Lesson 12
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Lesson Map

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

Topic A: Piecewise Functions

Topic B: Absolute Value Functions

Topic C: Function Transformations

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