Introduction to Graphic Design
Fancy Functions Inc. is hiring you to create a logo for their company. Your task is to create an image that could be used as the logo for a new product/service. The challenge is that Fancy Functions is a very small company and cannot afford expensive computers; therefore, your image must be created using the limitations of the graphing calculator, only 10 equations. Concepts
Function Transformations
Radical, power, exponential, logarithmic, polynomial and parent functions
Objectives Interpret constants, coefficients,
and bases in the context of the problem
Use calculator notation to make graphing more efficient
Materials
TI 83 or TI84 Calculator Graph paper imagination
Examples of Student Work
Strategies for graphing lines
Part 1
To get started, create the given picture on your calculator:
You could graph 4 separate equations:
Y1= -X+3
Y2= X+3
Y3= -X-3
Y4= X-3
Try to use the minimum equations necessary, because your creativity will be limited to the number of equations
you can key into your calculator…
Using this window:
one suggestion is:
one equation for 3 xy and
another equation for 3 xy
How about another way?
Try: 3 xy and reflect that over the x-axis
)x(f which is 3 xy
but we could enter it in the calculator as .12 yy
Type
Another more efficient method is: y = 3 x
This uses one space for the two equations.
Enter the in calculator language as {1,-1}.
SAVE YOUR WORK OFTEN
I recommend saving your work often. Store the
picture to a graph database (GDB). This stores
the graphing mode,
window variables,
format settings,
all functions in the Y= editor and the
selection status of each and
graph style for each Y= function.
To store as a GDB select
o 2nd Prog (Draw)
o STO
o 3:StoreGDB o Assign a number from 0 to 9
o Press Enter to store the current
database to the specified GDB variable.
To recall your GDB, select 4:RecallGDB from the
DRAW STO menu. Enter the number (from 0 to 9)
of the GDB variable to which you stored the graph
database. Press Enter.
After you have saved, clear your y=
You should have not a graph….
Recall your GDB, and your graph and your
equations should come back!
If borrowing a calculator, write down
your equations before leaving!!!
Part 2 Start a new picture, with a clean graph.
Adjust the window so the circle will be round.
X to Y ratio must be close to 3:2
(zoom, 4: decimal gets this window)
Next graph the circle (not a function!) 2 2( 3) ( ) 1x y
To enter it into the calculator, you need to solve for y…
So 21 ( 3)y x would be
2{1, 1}( (1 ( 3) ))y x
Variations on circles are given below:
Notice I used transformations (or variations) of Y1
to save key strokes.
Save this as a different GDB.
Clear the graphs and we will try another picture.
Part 3
Using a basic circle: 122 yx and variations, graph:
Choose your expression:
Write your equations in traditional form, change to y= if necessary
Key it efficiently into your calculator.
or or ??
Last Step
Once Your log is created:
Turn your graph paper version into an advertisement for Fancy Functions new product/service.
An example of a student project follows.
X to Y ratio in the window must be close to 3:2 or 1.5 so the circle will be round.
This one is 18:14 reduced to 9:7 approx 1.3 which is close enough.
Compare this to the following rubric to help get a feel for what will be expected on your project.
*** Please note, your completed project must include a graph paper version and all equations with work
showing how you solved for y and labeled as to what part of the picture each equation represents.
If you use the same shape in a different place, you may demonstrate your knowledge of shifting
functions instead of writing a new equation. (This would be considered a good thing and scored as a component
of “originality/difficulty” on the rubric).
Fancy Functions Feline Feast
Helps your kitty maintain a healthy digestive track
Graphic Design Project
EQUATION “Picture Part”
Y1=
Y2=
Y3=
Y4=
Y5=
Y6=
Y7=
Y8=
Y9=
Y0=
Graphic Design Project
EQUATION “Picture Part”
Y1=
Y2=
Y3=
Y4=
Y5=
Y6=
Y7=
Y8=
Y9=
Y0=
Graphing Piecewise-Defined Functions
You can use your graphing calculator to graph so-called “piecewise-defined” functions, such as:
Using the key, you enter the two “pieces,” one as Y1 and the other as Y2. When you are finished, they will look like this:
Y1 = 2X-2/(X<2)
Y2 = X^2-8/(X>2)
Notice the “slash” and the inequality in parentheses after each function. The slash is merely the division symbol and is entered simply
by pressing the key. Likewise for the parentheses.
To get the inequality symbols, press (gotten by pressing ) which will give you this screen:
Then simply select the desired inequality. If you do all this correctly, the screen should now look like this:
Enter the second function in a similar manner. The screen should now look like this:
Pressing the key yields the following result:
“DOUBLE” INEQUALITIES
With one addition, the same technique can be used to graph a function (or a piece of a function) whose domain is defined by a so-
called double inequality, such as:
The first thing that must be done is to split the double inequality into two separate inequalities joined by a logical and:
We enter the function into the same as before, and when we get to the logical and, we need to access the list of logical operators.
As before, press (gotten by pressing ), then use the right arrow key ( ) to move to the LOGIC screen:
Select the appropriate logical operator (in this case and) and proceed as before. The screen and the resulting graph should look
like those shown below:
Using the or operator, you can also graph functions such as:
Using the same techniques as above, the screen and the resulting graph should look like those shown below:
Graphing a Vertical Line (without using DRAW)
Both Clasic Mode and MathPrint Mode.
It is possible to draw vertical lines using the DRAW commands. Unfortunately, lines drawn with these
commands cannot utilize any of the graphing features such as intersect, etc.
There is a way to "fake" the calculator into producing a somewhat "workable" vertical line.
To graph the vertical line x = 5:
Y1 = A Big Number (x - 5)
where "A Big Number" is around 1,000,000.
The intersection option can be engaged.
Rationale:
You must solve these equations for ‘Y’ in before they can be entered into the calculator.
Fancy Function Inc. Project Name ___________________________________
PROJECTS DUE by December 10, 2015. Use the above rubric as a guide in completing your project. The rubric clearly states, that you need to draw your logo on a coordinate plane with a logo slogan for its advertisement. Professionally finished means that it is colored and the slogan is neatly written or typed in a manner similar to what you would see in a magazine advertisement. Your project must also include the ten functions as typed in your calculator. You also must have clearly labeled axes so that I can see if your window was adjusted. You may use the tables and grid included in the packet, but many students opt to be more creative in demonstrating all components.
0 1 2 3 4 5
Timeliness (includes check up
dates)
More than
4 days late 4 days late 3 days late 2 days late 1 day late On time
Precision
more than
one major
error or 3
minor
errors
3 minor errors
or 1 major
error
2 minor errors 1 minor error
All equations
match sketches,
no stray lines,
intersections
appropriate
Originality/
Difficulty/
Creativity
boring below average average above average Well done!
Quality &
Quantity of
equations
2 or fewer
types of
equations
without
shading or
piecewise-
defined
-2 types of
equations
with
shading &
piecewise-
defined
-at least 3
transformed
parent
functions
-3 types of
equations
without
shading or
piecewise-
defined
-at least 4
transformed
parent
functions
-3 types of
equations
with shading
& piecewise-
defined
-at least 5
transformed
parent
functions
-4 types of
equations
-one advanced
equation
without shading
& piecewise-
defined
-at least 6
transformed
parent functions
- more than 4
types of
equations
-one advanced
equation with
shading &
piecewise-
defined
-at least 7
transformed
parent functions
Follow
directions on
paper version
no paper
component
s
3 parts
missing
2 parts
missing 1 part missing
Graphs on graph
paper
w/appropriate
window &
points.
Equations
labeled with
“picture part”.
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ent
Picture with
no slogan,
not
professional
ly finished
Picture with
no slogan
Picture with
slogan, not
professionally
finished
Picture with
slogan
professionally
finished