MathematicsLinear and Exponential Functions

TCSS Emblem

[ Curriculum | Teacher Resources | Administrators | Academic Coaches ]


Unit Information

Content Map: Linear and Exponential Functions

EOCT STUDY GUIDE - UNIT 3

CCGPS Unit Standards or Troup County Version (TCV):

  • MCC9-12.A.REI.10 Understand that the graph of an equation in two variables is the set of all its solutions plotted in  the coordinate plane curve (which could be a line).

  • MCC9-12.A.REI.11 Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equations f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations.

  • MCC9-12.A.SSE.1 Interpret expressions that represent a quantity in terms of its context.

  • MCC9-12.A.SSE.1a Interpret parts of an expressions, such as terms, factors, and coefficients. (Emphasis on linear expressions and exponential expressions and exponential expressions with interger exponents.)

  • MCC9-12.A.SSE.1b Interpret complicated expressions viewing one or more of their parts as a single entity. (Emphasis on linear expressions and exponential expressions and exponential expressions with interger exponents.)

  • MCC9-12.F.IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs show key features including: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. (Focus on linear and exponential.)

  • MCC9-12.F.IF.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. (Focus on linear and exponential.)

  • MCC9-12.F.IF.6 Calcuclate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. (Focus on linear functions and intervals for exponential functions whose domain is a subset of the integer.)

  • MCC9-12.F.IF.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. (Focus on linear and exponential functions, Include comparisons of two functions presented algebraically.)

  • MCC9-12.F.IF.7a Graph linear functions and show intercepts, maxima, and minima.

  • MCC9-12.F.IF.7e Graph exponential showing intercepts and end behavior.

  • MCC9-12.F.IF.9 Compare properties of two functions each represented in a different way(algebraically, graphically, numerically in tables, or by verbal descriptions).

    MCC9-12.F.BF.1 Write a functions that describes a relationship between two quantities. (Linear and Exponential)

  • MCC9-12.F.BF.1a Determine an explicit expression, a recursive process, or steps for calculation from a context. (Linear and Exponential)

  • MCC9-12.F.BF.1b Combine standard function types using arithmetic operations. (Linear and Exponential)

  • MCC9-12.F.BF.2 Write arithmetic and geometric sequences both recursively and with explicit formula, use them to model situations, and translate between the two forms.

  • MCC9-12.F.BF.3 Identify the effect on the graph if 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. (Focus on vertical translations of graphs of linear and exponential functions. Relate the vertical translation of a linear function to its y-intercepts.

  • MCC9-12.F.LE.1 Distinguish between situations that can be modeled with linear functions and with exponential functions.

  • MCC9-12.F.LE.1a Prove that linear functions grow by equal differences over equal intervals and that exponential functions grow by equal factors over equal intervals.

  • MCC9-12.F.LE.1b Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.

  • MCC9-12.F.LE.1c Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.

  • MCC9-12.F.LE.2 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (including reading these from a table).

  • MCC9-12.F.LE.3 Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly.

  • MCC9-12.F.LE.5 Interpret the parameters in a linear or exponential function in terms of a context. (Limit exponential functions to those of the form f(x) = b^x + k.)

Prerequisites: As identified by the CCGPS Frameworks

  • U

Unit Length: 36 days

Unit Essential Questions:

  • How do I use graphs to represent and solve real-world equations and inequalities?

  • Why is the concept of a functions important and how do I use function notation to show a variety of situations modeled by functions?

  • How do I interpret functions that arise in applications in terms of context?

  • How do I use different representations to analyze linear and exponential functions?

  • How do I build a linear or exponential function that models a relationship between two
    quantities?

  • How do I build new functions from existing functions?

  • How can we use real-world situations to construct and compare linear and exponential models and solve problems?

  • How do I interpret expressions for functions in terms of the situation they model?

Unit Vocabulary: Reasoning with Equations & Inequalities Vocabulary

Resources by Concept: (click on a concept)

Concept 1: Represent and solve equations and inequalities graphically.
Resources:
  • McDougal Littell, Math 2, Lessons 4.4-4.5
  • McDougal Littell, Alg 1, Section 1.2, 4,6, 4.7
  • ABC Math II EOCT Section 10.8
  • McDougall Littell, Math 1, Lessons 1.2-1.3, 1.6-1.7
  • ABC Math I EOCT, Sections 1.1-1.5
  • Carnegie, Georgia Math 2, Lessons 8.2-8.3
  • America's Choice, Math 2 - Piecewise, Exponential Lessons 9-10, pages 43, 49
Tasks:
These tasks were taken from PARCC or the CCGPS Frameworks. The tasks cover multiple standards and may be used as teaching strategies or as culminating activities.
Back to Concepts  |  Back to Top
Concept 2: Understand the concept of a function and use function notation.
Resources:
  • McDougal Littell, Math 1, Lessons 1.2-1.3, 1.7, 3.13
  • ABC Math 1 EOCT, Sections 1.1, 1.2-1.5, 1.7
  • McDougal Littell, Math 2, Lessons 4.7, 4.9
Tasks:
These tasks were taken from PARCC or the CCGPS Frameworks. The tasks cover multiple standards and may be used as teaching strategies or as culminating activities.
Back to Concepts  |  Back to Top
Concept 3: Interpret functions that arise in applications in terms of the context.
Resources:
  •  McDougal Littell, Math 1, Lesson 1.2-1.8
  •  McDougal Littell, Math 2, Lessons 4.4-4.5 (Exponenetial)
  • America's Choice, Algebra in Context, Bridge to Georgia Math III, Lesson 1
  • America's Choice, Function Families (Linear/Exponential)
  • Coach, Math 1, Lesson 8, 9, 11
  • America's Choice, Georgia Math I Support, Lesson 16-17, Page 83
  • ABC Math I EOCT, 2.5, 2.6
  • McDougal, Algebra 1, 4.4
Tasks:
These tasks were taken from PARCC or the CCGPS Frameworks. The tasks cover multiple standards and may be used as teaching strategies or as culminating activities.
Back to Concepts  |  Back to Top
Concept 4: Analyze functions using different representations.
Resources:
  •  McDougal Littell, Math 1, Lesson 1.2-1.6, 1.8 (Linear)
  • McDougal Littell, Math 2, Lesson 4.4-4.5 (Exponential)
  • Carnegie, Math 2, Chapter 8, all (Exponential)
  • McDougal, Algebra 1, 4.2
  • ABC Math 1 EOCT, 2.5-2.6
  • Holt, Algebra 1, 4.3-4.4
  • America's Choice, Math 2 Support; Piecewise, Exponential, Inverse, Lesson 7
Tasks:
These tasks were taken from PARCC or the CCGPS Frameworks. The tasks cover multiple standards and may be used as teaching strategies or as culminating activities.
Back to Concepts  |  Back to Top
Concept 5: Build a function that models a relationship between two quantities.
Resources:
  •  McDougal Littell, Math 1, page 6, lesson 1.1, Problem Solving Workshop; Lesson 3.13
  • ABC Passing the Georgia Algebra 1 EOCT, Chapter 4
  • McDougall Littell, Math 2, Lesson 4.2 (w/o Compositions), 4.7-4.9
  • Holt, Algebra 2, 11.1-11.6
  • Coach, Math I, Lesson 12
Tasks:
These tasks were taken from PARCC or the CCGPS Frameworks. The tasks cover multiple standards and may be used as teaching strategies or as culminating activities.
Back to Concepts  |  Back to Top
Concept 6: Build new functions from existing functions.
Resources:
  •  McDougal Littell, Math 1, Lesson 1.7
  • McDougal Littell, Math 2, Lesson 2.4
  • America's Choice, Bridge to Math 3, Algebra in Context, Lessons 8-11
  • ABC, Math 1, 13.1-13.2
  • ABC Math 1 Support, 13.1-13.3
  • Coach, Math 1, Book 1, Lesson 28
  • Holt, Algebra 2, 2.7
Tasks:
These tasks were taken from PARCC or the CCGPS Frameworks. The tasks cover multiple standards and may be used as teaching strategies or as culminating activities.
Back to Concepts  |  Back to Top
Concept 7: Construct and compare linear and exponential models and solve problems.
Resources:
  •  McDougal, Algebra 1, Sections 5.2-5.3, 8.5-8.6
  • Visual Approach to Functions, Van Dyke, Unit 2-3
  • ABC, Algebra 1 EOCT, Lesson 11.11
  • ABC, Math II EOCT, Section 10.8
Tasks:
These tasks were taken from PARCC or the CCGPS Frameworks. The tasks cover multiple standards and may be used as teaching strategies or as culminating activities.
  • Illustrations: Interesting Interest Rate - Teacher Version
  • Illustrations: Exponential Functions - Teacher Version
  • Illustrations: Doubling Your Money - Teacher Version
  • Illustrations: 2 Points define Exponential I - Teacher Version
  • Illustrations: 2 Points define Exponential II - Teacher Version
  • Illustrations: Sandia Ariel Tram - Teacher Version
  • Illustrations: Rumors - Teacher Version
  • CCGPS Frameworks:
  • Community Service, Sequences, and Functions - Student Version | Teacher Version
  • Building and Combining Functions - Student Version | Teacher Version
  • Summing it up: Putting the "Fun" in Functions - Culminating Function - Student Version | Teacher Version

 

Back to Concepts  |  Back to Top
Concept 8: Interpret expressions for functions in terms of the situation they model.
Resources:
  •  McDougal , Algebra 1, section 1.2
  • ABC Math II EOCT, Section 10.8
Tasks:
These tasks were taken from PARCC or the CCGPS Frameworks. The tasks cover multiple standards and may be used as teaching strategies or as culminating activities.
Back to Concepts  |  Back to Top

Quick Links

6-12 Resources Home

Ga. Dept. of Educ.

georgiastandards.org

Instructional Tools

Planning Templates

TCSS Home

Thinkgate Resources

Web Resources

[   Home  |   Academic Coaches  |   Curriculum |   Teacher Resources | Administrators  ]