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.
Pacing: 18 instructional days (16 lessons, 1 flex day, 1 assessment day)
This assessment accompanies Unit 5 and should be given on the suggested assessment day or after completing the unit.
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Internalization of Standards via the Unit Assessment
Internalization of Trajectory of Unit
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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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Key: Major Cluster Supporting Cluster Additional Cluster
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