Functions and Transformations

Lesson 16

Math

Unit 5

9th Grade

Lesson 16 of 16

Objective


Apply transformations to 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.

Foundational Standards

  • 8.F.B.4
  • 8.G.A.3

Criteria for Success


  1. Describe multiple transformations of a function.
  2. Use points on the original function to transform the graph of a piecewise function.
  3. Write the equation, in function notation, for a graph that represents multiple transformations of a function. 

Tips for Teachers


Anchor Problem #2 requires students to have access to computers. 

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Anchor Tasks

25-30 minutes


Problem 1

The graph $${y=f(x) }$$ of a piecewise{ f}unction $${ f}$$ is shown. The domain of $$f$$ is $${-5≤x≤5}$$, and the range is $${-1≤y≤3}$$.

  1. Mark and identify four strategic points helpful in sketching the graph of $$y=f(x)$$.

  1. Sketch the graph of $$y=2f(x)$$ and state the domain and range of the transformed function. How can you use part (a) to help sketch the graph of $$y=2f(x)$$?
  2. A horizontal scaling with scale factor $${{1\over2}}$$ of the graph $$y=f(x)$$ is the graph of $$ y=f(2x)$$. Sketch the graph of $$ y=f(2x)$$ and state the domain and range. How can you use the points identified in part (a) to help sketch $$ y=f(2x)$$?

Guiding Questions

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References

EngageNY Mathematics Algebra I > Module 3 > Topic C > Lesson 20Exploratory Challenge 2

Algebra I > Module 3 > Topic C > Lesson 20 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..

Problem 2

Use the Desmos activity Transformations Practice.

For each transformation, write an equation that represents the blue graph, a transformation of the graph of $${ f(x)}$$.

Guiding Questions

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References

Desmos Transformations Practice

Transformations Practice by Bonnie Davis is made available by Desmos. Copyright © 2017 Desmos, Inc. Accessed May 10, 2018, 2:06 p.m..

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


The graph of a piecewise function $$f$$ is shown below. Let: 

$$p(x)=f(x-2)$$
$$q(x)={1\over2} f(x-2)$$
$$r(x)={1\over2} f(x-2)+3$$

Graph $${y=p(x)}$$, $${y=q(x)}$$, and $${y=r(x)}$$ in the same coordinate plane as the graph $$y=f(x)$$.

References

EngageNY Mathematics Algebra I > Module 3 > Topic C > Lesson 20Exit Ticket

Algebra I > Module 3 > Topic C > Lesson 20 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.

Lesson Map

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

Topic A: Piecewise Functions

Topic B: Absolute Value Functions

Topic C: Function Transformations

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