UOP – Art with graphs
Invitation
Functions are an important part of high school mathematics curriculum. Students learn
about various functions such as linear, quadratic, exponential, logarithmic and
trigonometric functions in Algebra II. Functions have a lot of applications in real life.
They provide mathematical models for many real life phenomenon or situations. Students
need to understand the functions and their graphs very well. They should have a clear
understanding of the impact of changing various components of a function, on the graph
of a function. They should understand how to translate the graphs, how to shrink or
expand them and how to rotate them. With a thorough understanding of the functions and
their graphs, students will be able to appreciate the powerful applications of functions to
real life situations.
This assignment has been created with the purpose of developing a deeper understanding
of functions and their graphs. Essential questions are:
 How can we create art or picture using parts of graphs of various functions
learned so far in Algebra II?
 How can we achieve translation (vertical or horizontal) of graphs in co-ordinate
plane, by manipulating the functions?
 How can we achieve shrinking/expansion of graphs in co-ordinate plane, by
manipulating the functions?
 How can we achieve rotation of graphs in co-ordinate plane, by manipulating the
functions?
 How can knowledge of domain and range of a function help us select only a part
of the graph?
Tasks
Students will be asked to create a picture of their choice using graphs of various functions
covered in Algebra II course so far.
Standards
Following State of California Algebra II (mathematics) content standards will be
addressed during the project.
 2.0 Students solve systems of linear equations and inequalities by substitution,
with graphs, or with matrices.
 9.0 Students demonstrate and explain the effect that changing a coefficient has on
the graph of quadratic functions; that is, students can determine how the graph of
a parabola changes as a, b, and c vary in the equation y = a(x-b)2 + c.
 12.0 Students know the laws of fractional exponents, understand exponential
functions, and use these functions in problems involving exponential growth and
decay.
Interactions
Teacher will introduce the graphing software called ‘Grapher’ available on iBook
laptops. Teacher will also review previously learned linear, quadratic, exponential, and
log functions. Following the review, students will work on the laptops to create a picture
using multiple function graphs. Each student will have his/her own laptop to work on.
Each student will submit an electronic copy of their work to be reviewed and graded by
the teacher.
Situations
The activity will take place over three days – three 55 min class periods in all Algebra II
classes. Day 1 is reserved for review of functions and graphing software. On day 2 and 3,
students will work on the project in class. Each student will have a laptop to work on.
Each laptop will have the grapher utility available on them. Students will save their
unfinished work in their digital locker provided on the school district server. Final
submission of the project will be done by turning an electronic copy of the picture (in
grapher software format as well as jpeg file) into the teachers digital drop box.
Assessment
The electronic copy of the picture along with the list of functions used will be graded by
the teacher as per the rubric provided.
Tools
Tools required for the task are:
 Laptops with Grapher software
 Student handout explaining the task and rubric
Name :______________________________
Art with graphs
Task:
You are going create a picture (work of art) using graphs of functions studied so far
namely linear, quadratic, and exponential using grapher software.
You are going to use restricted domain to get only a part of the graph of a function.
Final product to be turned in is the grapher file and a jpeg image file. Use the same
name for both the files.
For final submission, files (both) should be copied to teacher’s drop-box on the
school server by the end of the period on 02/06/09.
Details:
Your picture should be made up of at least 2 types of functions.
There should be at least 4 functions in the picture.
If you are using linear functions, at least one line has to be a slanting line (other than
horizontal or vertical line).
The picture should not be centered at the origin, or be symmetric about the X-axis or
the Y-axis. Move the picture to any one quadrant. So if you are using a quadratic
function, use translation to move the parabola horizontally and/or vertically.
Put a title for the picture and also write your name on the picture. Also, label the
graphs with the functions used.
Instructions to save your work-in-progress picture on the server:
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From the desktop click on Go/Connect to server.
In the server address box type in 10.221.4.11
Your login name is first letter of your first name and 5 letters of your last
name.
Password is last four digits of your student id.
This will get you into your server space. Go to the Documents directory and
save your file there.
After you are done saving the file, drag your folder icon from the desktop into
the trash can before shutting down the machine.
Instructions to submit your project in teacher drop-box:
On the last day of project, 10 minutes before end of class save your Grapher file on
the desktop. Again save this as a jpeg file (on the desktop) by using File/Export from
the top menu in Grapher. To submit both the files to the teacher follow these
instructions:
 Log into your server folder as explained before.
 Go to the directory labeled as Teachers. Then click on the directory labeled
CHANDV534.
 Next click on folder labeled Public and then click on folder labeled Dropbox.
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Drag both your files from the desktop into this Dropbox folder.
Drag your folder icon from the desktop into the trash can before shutting down
the machine.
Return this sheet in the bin to receive a score for your project.
Rubric:
Number of
functions
used
Types of
functions
used
Restricted
domain
Title and
Name
Creativity
4
At least four
functions are
used
3
Two
functions
used
correctly.
3
Domain used
correctly for
smooth finish
1
Yes
3
Three
functions are
used
2
One function
used correctly
2
Two functions are
used
2
Domain used
somewhat
correctly.
0
No
1
4
Very artistic
picture/object
3
Meaningful
picture
1
One
function is
used
1
2
Somewhat
meaningful
1
Picture/object is not
clear.
Total score possible = 15 points
For Extra Credit, use all three functions ( 3 points)
For late submissions, 10 % score will be deducted for each day.