Curriculum / Math / 9th Grade / Unit 5: Functions and Transformations / Lesson 16
Math
Unit 5
9th Grade
Lesson 16 of 16
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Apply transformations to functions.
The core standards covered in this lesson
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.
The foundational standards covered in this lesson
8.F.B.4 — Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.
8.G.A.3 — Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
Anchor Problem #2 requires students to have access to computers.
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Tasks designed to teach criteria for success of the lesson, and guidance to help draw out student understanding
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 $${-1≤y≤3}$$.
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..
Use the Desmos activity Transformations Practice.
For each transformation, write an equation that represents the blue graph, a transformation of the graph of $${ f(x)}$$.
Transformations Practice by Bonnie Davis is made available by Desmos. Copyright © 2017 Desmos, Inc. Accessed May 10, 2018, 2:06 p.m..
A set of suggested resources or problem types that teachers can turn into a problem set
Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
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 $$y=f(x)$$.
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 15
Topic A: Piecewise Functions
Write equations and graph linear relationships with different domains.
A.CED.A.1 A.CED.A.2 A.CED.A.3 F.IF.B.5 F.IF.C.7
Graph piecewise functions presented algebraically and write piecewise functions from graphs.
F.IF.A.2 F.IF.B.4 F.IF.C.7.B
Evaluate a piecewise function written algebraically, with and without context.
A.SSE.A.1.A F.IF.A.1 F.IF.A.2
Write and graph piecewise functions from contextual situations.
A.CED.A.2 A.CED.A.3 F.IF.B.5
Graph, evaluate, and write step functions, with and without context.
A.CED.A.3 F.IF.A.1 F.IF.C.7.B
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Topic B: Absolute Value Functions
Graph absolute value functions in the coordinate plane and identify domain and range.
F.BF.B.3 F.IF.B.4 F.IF.B.5 F.IF.C.7.B F.IF.C.9
Identify the solutions to an absolute value equation.
A.REI.A.1 A.REI.D.11
Solve absolute value equations algebraically and identify extraneous solutions.
A.REI.B.3
Identify the solution(s) to an absolute value inequality.
A.REI.A.1 A.REI.B.3 A.REI.D.11 F.IF.B.4 F.IF.C.7.B
Solve absolute value inequalities algebraically and verify graphically.
Identify solutions to a system of absolute value and linear functions graphically and algebraically.
A.REI.A.1 A.REI.C.6 A.REI.D.11
Topic C: Function Transformations
Identify and describe vertical translations of functions.
F.BF.B.3 F.IF.B.4 F.IF.B.5
Identify and describe horizontal translations of functions.
F.BF.B.3 F.IF.B.5
Identify and describe vertical scaling of functions, including reflections over the $$x$$-axis.
Identify and describe horizontal scaling of functions, including reflections over the $$y$$-axis.
F.BF.B.3
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