FRANCES PERKINS ACADEMY
Teacher:
Mr. Kandov
Subject:
Algebra II
Grade
9-12
Date:
Unit 1 – Functions, Equations, and Graphs
Lesson # 4
Graphing Absolute Value Functions
Learning Objective:
I can graph absolute value functions in the coordinate plane
How do we graph an absolute value function after applying transformations to it?
Focus Question:
Please Do Now:
1. Take out your homework.
3-5 minutes
2. Switch it with a partner’s homework.
3. Check each other’s work for peer-to-peer assessment.
Unit:
Common
Core
Standards
F.BF.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.
Vocabulary Absolute value function, axis of symmetry, vertex.
Mini –
DISCUSSION
Lesson
Although students have dealt with absolute value functions in the past few days, they need
20 min
to become aware of certain aspects about them.
MODELING
Example 1
How do we write the function for the absolute value graph below:
f(x)=lxl – 4
FRANCES PERKINS ACADEMY
Example 2
Ask: What does the +2 inside the absolute value mean? How about the +3 on the outside?
Therefore, our vertex is at (-2,3) because the parent function was translated 2 left, 3 up.
Ask: What if we wanted to stretch the new function by the factor 6? Should I write that
our function is y=6lx+2l + 3 OR y= l6x+2l+3?
Keep in mind, when scaling the function with a stretch or compression, does the axis of
symmetry change (no)? Does the vertex change (no)?
YOU TRY! 2 examples:
Graph the function y=lxl + 2. How is it different from the parent function?
FRANCES PERKINS ACADEMY
DOK (Qstns for assessment & understanding)
Procedure:
1. Do Now (5 min): Peer-to-Peer
assessment.
1.
2. Discussion (3 min): New
vocabulary introduced.
2. Are absolute value functions linear functions? Explain why
or why not.
3. Mini-Lesson (20 min):
a. Model Example 1 (5 min)
b. Model Example 2 (8 min)
with student input.
3. In Example 1, as the parent function y=lxl is translated 4
units down, what happens to the y-coordinate of the vertex?
To the x-coordinate?
[y changed from 0 to -4. x didn’t change.]
4. Students Practice (5-7 min)
YOU TRY! (guided example 2).
4. Why can the graph of an absolute value function have more
than one x-intercept?
5. Activity (10-15 min) Students
pair up in groups to complete a
short activity sheet to practice
concept learned today.
5. What kinds of transformations affect the axis of symmetry?
[horizontal translation.]
6. Closing (5 min): Provide students
with summative organizer for
transformations applied to
absolute value functions so that
they may re-check their
classwork and be better prepared
for homework.
Activity (s)
Worksheet
10-15 min
Assessment
In Do Now, what was a common mistake that you or your
partner noticed?
6. Follow-Up: Do transformations of the form y=lxl + k affect
the axis of symmetry? Explain.
[No, the axis stays the same. But the vertex moves
up/down along the axis of symmetry.]
7. When applying a vertical stretch or compression, does the
axis of symmetry change? How about the vertex
coordinate?
[No.]
Walk-around during activity. Carefully listen for feedback responses from students during minilesson and Do Now discussion. Assess peer-to-peer review in the Do Now as well as the group
work making sure each student is productive in the team.
Closing
Differentiate
Looking at f(x)=alx-hl+k, ask students what does the a, h, and k do to graph of the function?
Challenge students to write the equation of a graph of an absolute value function:
FRANCES PERKINS ACADEMY
Grouping
Homework
Pair-Share groups of two.
Back of worksheet
Materials/Resources
Notes/reflection___mins What have you learned today? Read aloud responses to closing statements.
Reminders:
(Test/Quizzes dates)
Differentiation and Tiered Instructional Strategies
☐Materials at varied readability levels
☐Supplementary materials based on
student interest
☐Varied teaching modes
☐Anchor activities (Sponge activities)
☐Compacting
☐Tiered activities
☐Portfolios
☐DOK Questioning
Reflection
☐Flexible use of time
☐Video/audio notes (visual/verbal learners)
☐Graphic organizer
☐Jigsaw
☐Problem Based Learning
☐Stations
☐Learning contracts
☐Cooperative learning
☐Use of contemporary technology
☐Flexible grouping
☐Learning contracts
☐Literature Circles
☐Socratic Seminar
☐Think, Pair, share
☐ Workshop Model
☐Models of tasks at different levels
☐Cubing