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”.

Advertisement

No

advertisem

ent

Picture with

no slogan,

not

professional

ly finished

Picture with

no slogan

Picture with

slogan, not

professionally

finished

Picture with

slogan

professionally

finished