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 and

another equation for

How about another way?

Try: and reflect that over the x-axis
which is
but we could enter it in the calculator as Type

Another more efficient method is: y = 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
  • 2nd Prog (Draw)
  • STO
  • 3:StoreGDB
  • Assign a number from 0 to 9
  • 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!)

To enter it into the calculator, you need to solve for y…

So would be

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: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.

Without the graph paper component, this project would lose 10 of the 30 points!

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).

Graphic Design Project

EQUATION / “Picture Part”
Y1=
Y2=
Y3=
Y4=
Y5=
Y6=
Y7=
Y8=
Y9=
Y0=
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/(X2)

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.

0 / 1 / 2 / 3 / 4 / 5
Timeliness / 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 components / 3 parts missing / 2 parts missing / 1 part missing / Graphs on graph paper w/appropriate window & points.
Equations labeled with “picture part”.
Advertisement / No advertisement / Picture with no slogan, not professionally finished / Picture with no slogan / Picture with slogan, not professionally finished / Picture with slogan professionally finished

Fancy Function Inc. ProjectName ______

PROJECTS DUE by December 11, 2014.