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.
Math
Unit 5
9th Grade
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)
The following assessments accompany Unit 5.
Use the resources below to assess student mastery of the unit content and action plan for future units.
Internalization of Standards via the Unit Assessment
Internalization of Trajectory of Unit
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) |
Topic A: Piecewise Functions
Topic B: Absolute Value Functions
Topic C: Function Transformations
Key
Major Cluster
Supporting Cluster
Additional Cluster
CCSS.MATH.PRACTICE.MP1 — Make sense of problems and persevere in solving them.
CCSS.MATH.PRACTICE.MP2 — Reason abstractly and quantitatively.
CCSS.MATH.PRACTICE.MP3 — Construct viable arguments and critique the reasoning of others.
CCSS.MATH.PRACTICE.MP4 — Model with mathematics.
CCSS.MATH.PRACTICE.MP5 — Use appropriate tools strategically.
CCSS.MATH.PRACTICE.MP6 — Attend to precision.
CCSS.MATH.PRACTICE.MP7 — Look for and make use of structure.
CCSS.MATH.PRACTICE.MP8 — Look for and express regularity in repeated reasoning.
Unit 4
Linear Equations, Inequalities and Systems
Unit 6
Exponents and Exponential Functions