2016-2017 Curriculum Blueprint
Grade: 9-12
Course: Pre-Calculus
Approximate Time:
7 days
Module 7: Analyzing Logarithmic Functions
Learning Goal
The student is expected to use the change of
base formula and logarithmic properties to
evaluate logarithmic functions, analyze and
graph logarithmic functions, choose
appropriate quantities and interpret
parameters for modeling logarithmic
functions, and understand and use the
relationship between exponential functions
and logarithmic functions to solve equations
and real-world applications with and without
technology.
Essential Questions
Unit Overview
How can logarithmic functions be evaluated, analyzed, and
graphed?
2. What quantities and parameters should be considered when
modeling with logarithmic functions?
3. How are the properties of logarithms developed from laws
of exponents?
4. What is the relationship between exponential and
logarithmic functions?
5. What strategies are used to solve logarithmic equations and
their real-world applications?
Students will use the change of base formula and logarithmic
properties to evaluate logarithmic functions, solve problems
involving exponential growth and decay, analyze and graph
exponential and logarithmic functions, choose appropriate
quantities and interpret parameters for modeling exponential
and logarithmic functions, and understand and use the
relationship between exponential functions and logarithmic
functions to solve equations and real-world applications with and
without technology.
1.
Vertical Progression
MAFS.912.N-Q.1.2, F-IF.2.5, F-IF.3.7, F-IF.3.8, F-BF.2.3, F-BF.2.a, F-LE.1.4, F-LE.2.5: In Algebra 2, students worked on applications and how key features relate to characteristics of a
situation making selection of a particular type of function, used the Change of Base Formula, and explored logarithmic functions and their graphs.
Module Focus Standards
Module Topics
Essential Vocabulary
MAFS.912.N-Q.1.2: (DOK 2) Define appropriate quantities for the purpose of
descriptive modeling.
High School Flip Book
natural logarithm
expanding a logarithm
condensing a logarithm
MAFS.912.F-IF.2.5: (DOK 2) Relate the domain of a function to its graph and,
where applicable, to the quantitative relationship it describes. For example, if the
function h(n) gives the number of person-hours it takes to assemble engines in a
factory, then the positive integers would be an appropriate domain for the
function.
MAFS.912.F-IF.3.7: (DOK 2) Graph functions expressed symbolically and show
key features of the graph, by hand in simple cases and using technology for more
complicated cases.
a.
Graph linear and quadratic functions and show intercepts, maxima, and
minima.
b.
Graph square root, cube root, and piecewise-defined functions,
including step functions and absolute value functions.
Constructing, Graphing, and Interpreting
Logarithmic Models (N-Q.1.2, F-IF.2.5, F-IF.3.7,
F-IF.3.8, F-BF.2.3, F-BF.2.a, F-LE.1.4, F-LE.2.5)
Core Resource:
Sections 3.2, 3.3, 3.4, 3.5 (Textbook)
Additional Resource:
Sections 3.2, 3.3, 3.4, 3.5 (Learning Guide)
Module 3 Lesson 21– Engage NY
Exponentials and Logarithms I – Illustrative
Mathematics
Exponentials and Logarithms II – Illustrative
Mathematics
Rumors – Illustrative Mathematics
Logarithms Demystified – Illuminations
Higher Order Question Stems
 How should the graph of a logarithmic
function be sketched knowing its relationship
with an exponential function?
 What quantities and parameters should be
considered when modeling with logarithmic
functions?
 How does the relationship between
exponential and logarithmic functions
determine the properties of logarithms?
 How could you solve a logarithmic equation?
 Why would a change of base formula be
helpful, and how could the formula be
derived?
2016-2017 Curriculum Blueprint
Grade: 9-12
Course: Pre-Calculus
Approximate Time:
7 days
Module 7: Analyzing Logarithmic Functions
c.
Graph polynomial functions, identifying zeros when suitable
factorizations are available, and showing end behavior.
d.
Graph rational functions, identifying zeros and asymptotes when
suitable factorizations are available, and showing end behavior.
e.
Graph exponential and logarithmic functions, showing intercepts and
end behavior, and trigonometric functions, showing period, midline, and
amplitude, and using phase shift.
MAFS.912.F-IF.3.8: (DOK 2) Write a function defined by an expression in different
but equivalent forms to reveal and explain different properties of the function.
a.
Use the process of factoring and completing the square in a quadratic
function to show zeros, extreme values, and symmetry of the graph, and
interpret these in terms of a context.
b.
Use the properties of exponents to interpret expressions for exponential
functions. For example, identify percent rate of change in functions such
𝑡
as y =(1.02)𝑡 , y =(𝑜. 97)𝑡 , y =(1.01)12𝑡 , y =(1.2) ⁄10 , and classify them
as representing exponential growth or decay.
MAFS.912.F-BF.2.3: (DOK 2) Identify the effect on the graph of 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
MAFS.912.F-BF.2.a: (DOK 1) Use the change of base formula.
MAFS.912.F-LE.1.4: (DOK 2) For exponential models, express as a logarithm the
solution to 𝑎𝑏 𝑐𝑡 = d where a, c, and d are numbers and the base b is 2, 10, or e;
evaluate the logarithm using technology.
MAFS.912.F-LE.2.5: (DOK 2) Interpret the parameters in a linear or exponential
function in terms of a context.
Mathematical Practices
Link to Mathematical Practice Standards Rubric
MAFS.912.MP.2.1: Reason abstractly and quantitatively.
Formative Assessments:
Describe the Domain
Height vs Shoe Size
Carbon 14 Dating - CPALMS
 What real-world situations could be modeled
and solved using logarithmic functions?
Writing Connections
 Create a logarithmic function, and write a
detailed description of its graph.
 Describe the product rule, quotient rule, and
the power rule for logarithms and give an
example of each.
 Describe the change of base formula in
words, and give an example.
 Explain the constraints on the domains of
logarithmic functions.
 Describe the two basic types of logarithmic
equations and explain how to solve each type.
 Explain the types of behavior that is best
modeled by logarithmic functions.
Link to Webb’s DOK Guide
2016-2017 Curriculum Blueprint
Grade: 9-12
Course: Pre-Calculus
Module 7: Analyzing Logarithmic Functions
MAFS.912.MP.6.1: Attend to precision.
MAFS.912.MP.7.1: Look for and make use of structure.
Approximate Time:
7 days