Lesson Title: Exponential and Logarithmic Transformations
Date: _____________ Teacher(s): ____________________
Course: Common Core Algebra II, Unit 2
Start/end times: _________________________
Lesson Standards/Objective(s): What mathematical skill(s) and understanding(s) will be developed? Which
Mathematical Practices do you expect students to engage in during the lesson?
F.BF.B.3 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.
A.SSE.B.3. Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity
represented by the expression.
c. Use the properties of exponents to transform expressions for exponential functions.
MP5: Use appropriate tools strategically.
MP7: Look for and make use of structure.
MP8: Look for and express regularity in repeated reasoning.
Common Core Algebra II, Unit 2
Lesson Launch Notes: Exactly how will you use the first
five minutes of the lesson?
“Use a graphing utility to graph the following functions and
explain, in your own words, what each value does to
transform f(x) to g(x).”
f (x)  x
Lesson Closure Notes: Exactly what summary
activity, questions, and discussion will close the lesson
and connect big ideas? List the questions. Provide a
foreshadowing of tomorrow.
Compare these two functions. Which values transform
the function in similar ways?
2
f (x)  (x  5) 2  3
f (x)  3log(2(x  1))  4


g(x)  3 10 2( x 1)  4
After students complete, ask, “Why do you think the 3
and 2 do similar things just in different orders?”

Lesson Tasks, Problems, and Activities (attach resource sheets): What specific activities, investigations,
problems, questions, or tasks will students be working on during the lesson? Be sure to indicate strategic
connections to appropriate mathematical practices.
1.
2.
3.
4.
5.
Spend a few minutes discussing the warm-up to determine what they remember from Algebra 1. Have students
display their graphs using Ti-smartview, a document camera or the overhead. Also, have them explain what the
2
5 and 3 do to f (x)  x .
Ask the students if they remember any other ways to change the appearance of a graph. “Are their any other
2
places we can place a value to change the appearance of f (x)  x ?”
“We have been working with exponential and logarithmic functions. Do you think we can apply the warm-up to
x
build
 new functions for exponential functions? Example: y  2 ?” “Where do you think we could put these
values to create new functions (transform the original)?”
Have students get a computer and log into their
 accounts.
Once the students have logged in, direct them to the following links:
http://www.analyzemath.com/expfunction/expfunction.html

http://www.analyzemath.com/logfunction/logfunction.html
If students do not have access to computers, they can use a graphing calculator. They can change the
b(x c )
 d or f (x)  a log B (b(x  c))  d to determine what a, c, h,
different values of f (x)  aB
and k do to transform the graph. (MP5)
HCPSS Secondary Mathematics Office (v2.1); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student
achievement. Portsmouth, NH: Heinemann.

Lesson Title: Exponential and Logarithmic Transformations
Course: Common Core Algebra II, Unit 2
Date: _____________ Teacher(s): ____________________
Start/end times: _________________________
6. Assign students to groups of 4. Have half the groups focus on exponential functions and the other half focus on
logarithmic functions. The students will need to scroll down a little and click on the button that says “Click
Here to” underneath step 2 on the website.
7. Given them a minute to adjust and move the bars in the applet so that they know how it works. Give the
students “F.BF.B.3 Worksheet Exp and Log Transformations” and have the students work through it together.
(Look for evidence of MP5, MP7.)
8. As they work, periodically check on each group to make sure they are all on the right track. Since the students
may need to teach others how their values manipulated a graph, it is important that they clearly understand. As
you check on your students, check for understanding of MP8. Hopefully they will start seeing patterns as they
manipulate each characteristic.
9. Once each group completes their investigation, have the students from the exponential groups partner with
students from the logarithmic groups. The two that moved must learn as much as they can, and the 2 that stayed
need to teach their new members about their function. Give students a few minutes to take notes on their
worksheet. (Look for evidence of MP7.)
10. Once they have completed this phase, have the original groups rejoin. The students should take the opportunity
to help their group members understand both function types and how their graphs change. As they work
together, they should make connections between the transformations from Algebra 1 and with exponentials and
logarithmic functions. (Look for evidence of MP8.)
11. Start a whole group discussion on their results. Have the groups share with the class to make sure all students
agree and understand the different components for a transformation. Also, it is important for students to make
connections with how these transformations are similar to linear and quadratic models. For example, “In y = mx
+ b, the b value (y-intercept) is similar to a ______________, and the m (slope) is similar to
2
_________________. For quadratic models y  a(x  h)  k , k represents a ________________, h moves
the graph __________________, and a ____________________.” Make sure the students are filling in the
blanks so that they are demonstrating this connection to prior knowledge.
12. Have students complete the reflection portion of “F.BF.B.3 Worksheet Exp and Log Transformations.” (Look
for evidence of MP7, MP5.)

Evidence of Success: What exactly do I expect students to be able to do by the end of the lesson, and how will I
measure student success? That is, deliberate consideration of what performances will convince you (and any outside
observer) that your students have developed a deepened and conceptual understanding.
When given multiple variations of exponential and logarithmic functions, students will be able to determine how to
transform a graph as well as describe how the values shift a graph. After students complete the homework, collect it
and review student responses to determine how much additional time is required to complete the topic.
Notes and Nuances: Vocabulary, connections, anticipated misconceptions (and how they will be addressed), etc.
The purpose of the warm-up is to have students draw from prior knowledge (Algebra 1). They previously discussed
transformations with linear and quadratic functions and the hope is that the students remember some them and apply
them to exponential and logarithmic equations.
If you know that your computers have issues logging in, have students get computers as soon as they walk in to class
so they can start-up and be ready for the lesson. Also, the applet works best with Firefox. If the applet is not working
correctly, they can also click on the link given in step 1 on the website. This is an HTML format and should work.
From my experience with these applets, fractions do not work. Students will need to convert to decimals when
testing specific values.
Resources: What materials or resources are essential for
students to successfully complete the lesson tasks or
activities?
Homework: Exactly what follow-up homework tasks,
problems, and/or exercises will be assigned upon the
completion of the lesson?
HCPSS Secondary Mathematics Office (v2.1); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student
achievement. Portsmouth, NH: Heinemann.
Lesson Title: Exponential and Logarithmic Transformations
Date: _____________ Teacher(s): ____________________
http://www.analyzemath.com/expfunction/expfunction.html
Course: Common Core Algebra II, Unit 2
Start/end times: _________________________
Homework sheet provided.
http://www.analyzemath.com/logfunction/logfunction.html
Lesson Reflections: How do you know that you were effective? What questions, connected to the lesson
standards/objectives and evidence of success, will you use to reflect on the effectiveness of this lesson?
Are students able to graph a function without an electronic device?
Can they correctly label the different transformations of a graph?
Howard County Public Schools Office of Secondary Mathematics Curricular Projects has licensed this
product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.
HCPSS Secondary Mathematics Office (v2.1); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student
achievement. Portsmouth, NH: Heinemann.