Graphing Logarithmic Functions
Using Transformations
Presenter:
School Name:
District Name:
Guiding Teacher:
Time Frame:
Anthony Mussari
St. Joseph's Collegiate Institute
Buffalo City Schools
Mr. Thomas Quagliana
Two Days (Lecture and Assessment)
Grade level:
Course Name:
Student Total:
General Ability:
Tenth and Eleventh (Boys Only)
Algebra II & Trigonometry Honors
Sixty-Five
Accelerated / Advanced Placement
The Standard…
Standard: F-BF.3. Identify the effect on
the graph of replacing f(x) by f(x) + k,
k•f(x), f(k•x), and f(x + k) for specific
values of k (both positive and negative);
find the value of k given the graphs.
Mathematics NYS Common Core
The Standard…
Standard: F-BF.3. (Continued)
Experiment 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.
Mathematics NYS Common Core
The Learner Will Be Able To…
Identify the effect on the graph of f(x) for
specific values of k by replacing f(x) with
 f(x) + k
k• f(x)
f(k•x)
f(x + k)
In addition find the value/s of k given the
graph of f(x).
Essential Question???
What will happen to the graphs of yi = f(x) when
composed with a constant ki ?
Handout WRKSHT
Guiding Questions???
What are the characteristics of the parent function
yi = f(x)?
How does one read a graph?
When is it appropriate to use transformations?
Enduring Understanding!!!
Graphing with transformations can generate
images on a host of parent functions.
Different images provide unique inferences.
The Procedure!!!
Illustrate to the learner, by way of
guided notes and interactive
lecture, of how to Identify the
effect on the graphs of f(x) by
replacing f(x) with f(x) + k, k
f(x), f(kx), and f(x + k) for
specific values of k.
Note Packet
The Procedure!!!
A take-home assignment will
require the student to find and
state the equation of a logarithmic
function by identifying the effect
on the graph by replacing f(x)
with f(x) + k, k f(x), f(kx), and
f(x + k) for specific values of k.
Take-Home WRKSHT
The Procedure!!!
The Logarithmic Rubric and Quiz
# 3.8 will be used to formally
asses and quantify each of the
students’ understanding.
Rubric and Quiz
Student work, Developing.
Student work, Proficient.
Student work, Distinguished.
Student work, The Data.
Classifications
Number of
students
0
3
62
Pre-Instruction
Distinguished
Proficient
Developing
Percentage of
students
00.00 %
04.60%
95.40 %
Classifications
Number of
students
43
13
9
Post-Instruction
Distinguished
Proficient
Developing
Percentage of
students
66.15 %
20.00 %
13.85 %
Classifications
Distinguished
Proficient
Post
Pre
Developing
0
10
20
30
40
Number of Students
50
60
70
Modification Table.
Modification
Type
Instructional
Specific
Modification
Guided
Notes
Rationale for
Modification
Benefits of
Modification
Students
produce
complete and
accurate lecture
notes.
Students who
take accurate
notes and study
them later
consistently
receive higher
test scores than
students who
only listen to the
lecture and read
the text*.
GN increase
students’ active
engagement
with course
content.
* Heward, William L., Improving The Effectiveness Of Your Lectures. Retrieved from
http://ada.osu.edu/resources/fastfacts/Guided-Notes-Fact-Sheet.pdf (08 May 2012).
Reflection Table.
Peer Review
Suggestion
How do you plan
on eventually
integrating the
graphing
calculators into
the students’
learning?
Topic of
Suggestion
Technology
Integration
Rationale for
Suggestion
Evidence found in
the Learning
Experience
The NYS Common
Core addresses the
use of a calculator
Anticipatory Set:
or technology to
demonstrate the
effects of a
transformation.
Thank You!!!
To my peer reviewers,
Christopher, Shelly, Jessica,
Mary, Karissa, Meghan, Sarah,
and Dr. Arnold,
You all provided may useful comments, both
warm and cold, for which I would like to formally
thank you for.
This Presentation Has Been Brought To
You By….
Anthony J. Mussari
To contact via:
Post:
Anthony J. Mussari
c/o Daemen College
4380 Main Street
Amherst, NY 14226
E-Mail:
amussari@daemen.edu
Phone:
716.380.6313
Fin