Students review and extend the Algebra 1 skills of graphing, manipulating, and describing solutions in order to deepen their understanding of modeling situations using linear functions.
In Unit 1, Linear Functions and Applications, students review and extend the Algebra 1 skills of graphing, manipulating, and describing solutions to linear functions to deepen their understanding of modeling situations using linear functions. In this unit, students review concepts, such as using multiple representations, inverse, constraints, and systems, that are essential for studying polynomial, rational, exponential, and logarithmic functions, and trigonometric functions in later units through linear functions, a familiar and basic parent function.
Unit 1 begins with students translating between representations of linear functions to identify the strengths of each representation and to highlight features of linear functions. Inverse of linear functions is studied through contextual situations, to ensure that students grasp the symmetry between a function and its inverse, as well as connect the meaning of each variable and its role (dependent or independent) in the concept of inverse. Topics in this unit continue through systems—a concept that is very familiar to students. The focus in this section of the unit is again contextual as well as procedural to allow students to be fully fluent in solving systems algebraically, graphically, with three variables, and with absolute value functions, an application of a linear function. Students review piecewise functions through a linear lens to bolster their facility with constraints and analysis of functions in preparation for nonlinear piecewise functions. Students who are taking the pre-calculus portion of this course will continue on to compose functions within and outside of context to model and identify solutions to real-life scenarios.
As Algebra 2 progresses, students will draw on the concepts from this unit to find the inverse of functions, restrict domains to allow a function to be invertible, operate with various functions, model with functions, identify solutions to systems of functions graphically and algebraically, and analyze functions for their value and behavior. Mastering the skills in this unit will allow for students to have a solid framework to build upon when studying other functions.
Pacing: 15 instructional days (13 lessons, 1 flex day, 1 assessment day)
This assessment accompanies Unit 1 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 restriction | constraint | inverse functions |
inverse notation $${f^{-1}(x)}$$ | invertible functions | extraneous solution(s) |
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A.SSE.A.1.A
F.IF.B.4
F.IF.C.9
Identify features of linear functions from equations, verbal descriptions, tables, and graphs.
F.IF.A.2
F.IF.B.4
F.IF.B.5
Write linear functions that represent contextual situations.
A.CED.A.1
A.CED.A.4
Solve for a desired quantity in a linear function.
F.BF.B.4.A
F.BF.B.4.C
Find the inverse of a contextual situation graphically and describe the meaning of the function and its inverse.
F.BF.B.4.A
F.BF.B.4.B
F.BF.B.4.C
Find the inverse of contextual and non-contextual situations algebraically.
F.IF.B.5
A.CED.A.2
A.REI.C.6
Write a system of functions for contextual situations and solve algebraically. Describe the solutions in context of the problem.
A.REI.C.6
A.REI.D.11
Describe the number of solutions of a system of equations. Verify algebraically.
A.REI.C.6
Solve a system of three equations in three variables.
A.REI.D.11
Identify the solution to a system of an absolute value equation and a linear function algebraically and graphically.
F.IF.B.5
A.CED.A.3
A.REI.D.12
Graph and identify solutions to systems of linear inequalities.
A.CED.A.3
A.REI.D.12
Write systems of linear inequalities from a contextual situation.
Key: Major Cluster Supporting Cluster Additional Cluster
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