Curriculum  /  Math  /  9th Grade  /  Unit 5: Functions and Transformations  /  Lesson 13

Functions and Transformations

Lesson 13

Math

Unit 5

9th Grade

Lesson 13 of 16

Objective

Identify and describe horizontal translations of functions.

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.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.

Foundational Standards

  • 8.F.B.4
  • 8.G.A.3

Criteria for Success

  1. Identify when the graph of a function has been shifted horizontally, both in a graph and in an equation.
  2. Describe how to shift a function’s graph horizontally in a table of values or graphically.
  3. Draw graphs of functions that have been translated horizontally.
  4. Write equations, in function form, to represent graphs of functions that have been translated horizontally using h to represent the horizontal translation (i.e., $${f(x+h)}$$).
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Anchor Problems

Problem 1

Consider the two functions below. 

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

$${{g(x)}=|x-2|}$$

  1. Create a table of values for each function and use it to graph each function in the coordinate plane. 
  2. Looking at the tables and the graphs, what changed from the parent function, $${ f(x)}$$, to the new function, $${g(x)}$$? What is the same? 
  3. Look at the corresponding work in the Desmos activity, Introduction to Transformations of Functions, slides 2–5. 

Guiding Questions

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References

Desmos Introduction to Transformations of Functions — Slides 2-5

Introduction to Transformations of Functions by is made available by Desmos. Copyright © 2017 Desmos, Inc. Accessed May 10, 2018, 4:21 p.m..

Modified by Fishtank Learning, Inc.

Problem 2

Predict what the tables and graph would look like for each function below. Then refer to slide 6 in the Desmos activity Introduction to Transformations of Functions to try out other values for $$h$$.

  1.   $${y=|x-3|}$$
  2.   $${y=|x+4|}$$
  3.   $$y=|x-h|$$

A different parent function and transformations are shown below. Predict what each graph would look like. Then refer to slides 7–13 in the Desmos activity. 

  1.   $${y=x^2}$$
  2.   $${y=(x-2)^2}$$
  3.   $${y=(x+1)^2}$$
  4.   $$y=(x-h)^2$$

Guiding Questions

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References

Desmos Introduction to Transformations of Functions — Slides 6-13

Introduction to Transformations of Functions by is made available by Desmos. Copyright © 2017 Desmos, Inc. Accessed May 10, 2018, 4:21 p.m..

Modified by Fishtank Learning, Inc.

Problem 3

Describe how the graph of the parent function $${{ f(x)=|x|} }$$ is transformed to represent function 
$${g(x)=|x-1|+4}$$.

The graph of function $${ f(x)=|x|}$$ is translated $$8$$ units down and $$5$$ units to the right. Write a function $${j(x) }$$ that represents the transformed graph. 

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

Write the formula for the functions depicted by the graphs below.

  1.   $${f(x)=}$$
  2.   $${g(x)=}$$
  3.   $${h(x)=}$$

References

EngageNY Mathematics Algebra I > Module 3 > Topic C > Lesson 18 — Exit Ticket

Algebra I > Module 3 > Topic C > Lesson 18 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..

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 12

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Lesson 14

Lesson Map

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

Topic A: Piecewise Functions

Topic B: Absolute Value Functions

Topic C: Function Transformations

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