Unit Information
Content Map:
Linear and Exponential Functions
EOCT
STUDY GUIDE  UNIT 3
CCGPS Unit Standards or Troup County Version
(TCV):

MCC912.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).

MCC912.A.REI.11 Explain why
the xcoordinates 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.

MCC912.A.SSE.1 Interpret
expressions that represent a quantity in terms of its context.

MCC912.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.)

MCC912.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.)

MCC912.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.)

MCC912.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.)

MCC912.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.)

MCC912.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.)

MCC912.F.IF.7a Graph linear
functions and show intercepts, maxima, and minima.

MCC912.F.IF.7e Graph
exponential showing intercepts and end behavior.

MCC912.F.IF.9 Compare
properties of two functions each represented in a different
way(algebraically, graphically, numerically in tables, or by verbal
descriptions).
MCC912.F.BF.1 Write a
functions that describes a relationship between two quantities.
(Linear and Exponential)

MCC912.F.BF.1a Determine an
explicit expression, a recursive process, or steps for calculation
from a context. (Linear and Exponential)

MCC912.F.BF.1b Combine
standard function types using arithmetic operations. (Linear and
Exponential)

MCC912.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.

MCC912.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 yintercepts.

MCC912.F.LE.1 Distinguish
between situations that can be modeled with linear functions and with
exponential functions.

MCC912.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.

MCC912.F.LE.1b Recognize
situations in which one quantity changes at a constant rate per unit
interval relative to another.

MCC912.F.LE.1c Recognize
situations in which a quantity grows or decays by a constant percent
rate per unit interval relative to another.

MCC912.F.LE.2 Construct
linear and exponential functions, including arithmetic and geometric
sequences, given a graph, a description of a relationship, or two
inputoutput pairs (including reading these from a table).

MCC912.F.LE.3 Observe using
graphs and tables that a quantity increasing exponentially eventually
exceeds a quantity increasing linearly.

MCC912.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
Unit Length: 36
days
Unit Essential Questions:
How do I use graphs to represent and solve
realworld 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 realworld 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 4.44.5
 McDougal Littell, Alg
1, Section 1.2, 4,6, 4.7
 ABC Math II EOCT
Section 10.8
 McDougall Littell,
Math 1, Lessons 1.21.3, 1.61.7
 ABC Math I EOCT,
Sections 1.11.5
 Carnegie, Georgia Math
2, Lessons 8.28.3
 America's Choice, Math
2  Piecewise, Exponential Lessons 910, 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. 

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Concept 2: Understand the concept of a function and use function
notation. 
Resources: 

McDougal Littell, Math 1, Lessons 1.21.3, 1.7, 3.13

ABC Math 1 EOCT, Sections 1.1, 1.21.5, 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. 

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Concept 3: Interpret functions that arise in
applications in terms of the context. 
Resources: 
 McDougal Littell, Math 1, Lesson
1.21.8
 McDougal Littell, Math 2, Lessons
4.44.5 (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 1617, 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. 

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Concept 4: Analyze functions using different
representations. 
Resources: 
 McDougal Littell, Math 1, Lesson
1.21.6, 1.8 (Linear)
 McDougal Littell, Math 2, Lesson 4.44.5
(Exponential)
 Carnegie, Math 2, Chapter 8, all
(Exponential)
 McDougal, Algebra 1, 4.2
 ABC Math 1 EOCT, 2.52.6
 Holt, Algebra 1, 4.34.4
 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. 

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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), 4.74.9
 Holt, Algebra 2, 11.111.6
 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 811
 ABC, Math 1, 13.113.2
 ABC Math 1 Support, 13.113.3
 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
5.25.3, 8.58.6
 Visual Approach to Functions, Van Dyke,
Unit 23
 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

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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 

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