Chapter 5 – Linear Functions
Section 8 – Graphing Absolute Value Functions – Day 2
Class time: - 90 minutes (double period)
Grade Level: - 8th grade Algebra I Honors
Objectives: To visualize the horizontal translations as a means of transforming one graph into another.
Content Standard: 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.
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.★
b. Graph square root, cube root, and piecewise-defined functions, including step functions and
absolute value functions.
Materials: Textbook – Pearson Algebra I hard copy and online version, SMARTboard, SMARTboard
presentation, Calculators, Laptop Computers, Other.
Lesson Procedure:
 Review homework to check for understanding
 Review key concepts from the previous lesson and tell the students how it connects to today’s
lesson
 SMARTboard presentation to introduce the new lesson
 Introduce graphing absolute value functions on a graphing calculator
 Individual Practice – worksheet
 http://online.carnegielearning.com/ – preparation for NJASK exam from Carnegie Learning
Assessment: Homework: pg. 349 #15 -20 all, 24, 25, 28, 29, 31 – 34 (use calculator to graph)
First, students will check the homework using the online book with answers to the homework
assignment (displayed on the SMARTboard). When students are done with checking their answers I
will go over the exercises that they had problem with and didn’t get the correct answer.
After homework is checked we will one more time identify the translation of the parent function
y=|x| to y=|x|+k. Students should know that this is a vertical shift (over y – axis) according to the value
and sign of k. Next, I will turn on the projector with the presentation of a new lesson (see Attachment
1), which is a continuation of the lesson from the day before when we were talking about a vertical
translation.
The first slide has a question on top which asks what happens if we have an additional term inside
of the absolute value. How does that translate the parent function? Next we have two graphs showing
how the value inside the absolute value translates the parent function. To prove that we will make three
tables that will look as follows:
x
y=|x|
y
x
y=|x+2|
y
x
y=|x-2|
y
-1
=|-1|
1
-2
=|-2+2|=|0|
0
-2
=|-2-2|=|-4|
4
0
=|0|
0
-1
=|-1+2|=|1|
1
-1
=|-1-2|=|-3|
3
1
=|1|
1
0
=|0+2|=|2|
2
0
=|0-2|=|-2|
2
1
=|1+2|=|3|
3
1
=|1-2|=|-1|
1
2
=|2+2|=|4|
4
2
=|2-2|=|0|
0
This will prove that we shift/translate the graph along the x-axis by h units to the left or right.
However, unlike with the translation along the y-axis, now we shift the parent graph in opposite
direction from what the sign of h tells us.
Second slide models one example from the book and on the second part of the slide we will do
example 3. At this time I will ask the students to guide me through the problem, by telling me the next
step we should take.
Finally, on the last slide we have a problem that the students will work on at their desks and
then will come up and put it on the board. After that exercise we finish this presentation and I will give
the students a typed up instructions (see attachment 2) for graphing absolute value functions on
graphing calculators (TI-73 Explore). I will also model a problem – y=|x-1|, y=|x| + 2 – on the
SMARTboard using the software.
Worksheet (see attachment 3) that I will give the students next will be in a form of an
independent practice. They will do 4 assigned problems from the worksheet that will connect the two
lessons on graphing absolute value functions. When the students are done with graphing the four
functions we will go over their answers and I will answer questions. After that we will conclude the
lesson with repeating the characteristics for translations along x – axis and y – axis.
If there is time left over each students will get a laptop computer to go on Carnegie Learning
website to work on the lessons that are preparing them for NJASK exams. While the students work on
their online lessons I will walk around to make sure that they are on task and answer questions if there
are any.
Thorough the lesson I will use a formative assessment by observing the students work and
asking if anyone has any questions or concerns about what we are doing at the particular time. The
final assessment will be the homework which we will check and go over on Thursday.