Functions and Transformations

Lesson 6

Math

Unit 5

9th Grade

Lesson 6 of 16

Objective


Graph absolute value functions in the coordinate plane and identify domain and range. 

Common Core Standards


Core Standards

  • F.BF.B.3 — Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.
  • 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.B.5 — Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function. 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.
  • F.IF.C.9 — Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.

Foundational Standards

  • 8.F.B.4

Criteria for Success


  1. Graph a piecewise function that mimics an absolute value function.
  2. Graph an absolute value function using a table of values and compare to a piecewise function.
  3. Describe the domain and range of an absolute value function.

Tips for Teachers


Students will see examples of absolute value functions that have undergone transformations from the parent function $${f(x)=|x|}$$; however, students should graph these functions from either a table of values or using technology. Students will study function transformations in the next topic of this unit.

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Anchor Problems


Problem 1

Function $${{{g(x)}}}$$ is shown below.

$${{{g(x)}}}=|x|$$

  1. Graph $${{{g(x)}}}$$ using a table of values. Include negative and positive values. 
  2. Compare function $${{{g(x)}}}$$ to piecewise function $${ f(x)}$$, given below.

Guiding Questions

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Problem 2

Graph $${{g(x)}}$$, shown below, on a coordinate plane using a table of values. Then write a piecewise function, $${f(x)}$$, that would have the same graphical representation as $${{g(x)}}$$.

$${{g(x)}}=|x-5|$$

Guiding Questions

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Problem 3

Write a table of values for function $${f(x) }$$ below and then graph. Describe the domain and range.  

$${f(x)=-|x+2|+4}$$

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 function $${f(x)}$$ using a table of values. Define the domain and range of the function.

$${f(x)}=|x+2|-5$$

 

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.

  • EngageNY Mathematics Algebra I > Module 3 > Topic C > Lesson 15Problem Set, Question #6a-6e
  • Kuta Software Free Algebra 1 Worksheets Graphing Absolute Value Functions(Have students use a table of values to graph and then verify with technology; ask students to define the domain and range for each question, and for some questions have students write a corresponding piecewise function.)
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Lesson 5

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Lesson 7

Lesson Map

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

Topic A: Piecewise Functions

Topic B: Absolute Value Functions

Topic C: Function Transformations

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