Students take a deeper look at piecewise functions and absolute value functions, and study how transformations of functions can be identified graphically and represented algebraically.
In Unit 5, Functions and Transformations, students take a deeper look at piecewise functions and absolute value functions, and then study how transformations of functions can be identified graphically and represented algebraically. Throughout the unit, students will recall and utilize skills from eighth grade as they manipulate equations and inequalities, write equations from graphs, and solve systems of equations.
In Topic A, students recall from Unit 1 how a graph can depict different behaviors over different domains. They define these functions as piecewise functions and look at various real-world applications that can be modeled using piecewise and step functions.
In Topic B, students identify the graph of an absolute value function as a piecewise function. They solve absolute value equations and inequalities algebraically, and students also leverage their understanding of systems of equations to conceptualize their solutions graphically in the coordinate plane.
In Topic C, students use the absolute value function as a vehicle to understand, identify, and represent transformations to function graphs. Along the way, they also apply transformations to other parent functions and learn how the graph of any function can be manipulated in certain ways using algebraic rules.
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Domain/range | Absolute value inequality |
Piecewise function | Parent function |
Step function | Transformations of functions |
Absolute value functions | Translation (vertical and horizontal) |
Extraneous solution | Scaling (vertical and horizontal) |
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Internalization of Standards via the Unit Assessment
Internalization of Trajectory of Unit
This assessment accompanies Unit 5 and should be given on the suggested assessment day or after completing the unit.
F.IF.B.5
F.IF.C.7
A.CED.A.1
A.CED.A.2
A.CED.A.3
Write equations and graph linear relationships with different domains.
F.IF.A.2
F.IF.B.4
F.IF.C.7.B
Graph piecewise functions presented algebraically and write piecewise functions from graphs.
F.IF.A.1
A.SSE.A.1.A
F.IF.A.2
Evaluate a piecewise function written algebraically, with and without context.
F.IF.B.5
A.CED.A.2
A.CED.A.3
Write and graph piecewise functions from contextual situations.
F.IF.A.1
F.IF.C.7.B
A.CED.A.3
Graph, evaluate, and write step functions, with and without context.
F.IF.B.4
F.IF.B.5
F.IF.C.7.B
F.IF.C.9
F.BF.B.3
Graph absolute value functions in the coordinate plane and identify domain and range.
A.REI.A.1
A.REI.D.11
Identify the solutions to an absolute value equation.
A.REI.B.3
Solve absolute value equations algebraically and identify extraneous solutions.
F.IF.B.4
F.IF.C.7.B
A.REI.A.1
A.REI.D.11
Identify the solution(s) to an absolute value inequality.
A.REI.B.3
Solve absolute value inequalities algebraically and verify graphically.
A.REI.A.1
A.REI.C.6
A.REI.D.11
Identify solutions to a system of absolute value and linear functions graphically and algebraically.
F.IF.B.4
F.IF.B.5
F.BF.B.3
Identify and describe vertical translations of functions.
F.IF.B.5
F.BF.B.3
Identify and describe horizontal translations of functions.
F.IF.B.5
F.BF.B.3
Identify and describe vertical scaling of functions, including reflections over the $$x$$-axis.
F.IF.B.5
F.BF.B.3
Identify and describe horizontal scaling of functions, including reflections over the $$y$$-axis.
F.BF.B.3
Apply transformations to functions.
Key: Major Cluster Supporting Cluster Additional Cluster
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