Unit 3 Day 4

Warm-Up 1. Write the Now/Next Function Rule for 3, -9, 27, -81, …

2. Write the Input/Output Function Rule for the table to the right:

3. In right triangle ABC, side AC is longer than side BC. The boxed numbers represent the possible side lengths of triangle ABC.

Identify three boxed numbers that could be the side

lengths of triangle ABC. Enter the number you chose to represent the length of each side.

 a. BC =_____ b. AC =_____ c. AB =_____

15 8 7 10 13 6

Input -1 -3 4 6

Output 1 3 -4 6

HW Check

On the lined side of the index card:

1. Create a table of Input/Output Values that can be represented by an equation

2. Give at least 4 terms in your sequence.3. Write your name on the lined side of the

index card. Ex.

Review of Input-Output Functions

Input (x)

Output (y)

-2 -2

0 0

1 1

3 3

Find a partner NOT at your table. 1. Write the partners name on the white

side of the index card.2. Have your partner create the now/next

function for your sequence.3. Partners turn in the index card to the

bin at the front of the room.

Equation: y = x

Partner’s Name

Secret Codes

You have studied many relationships between quantities. In this lesson you will learn about a special type of relationship called a function.

In this lesson you will● use a coding grid to write a coded

message● create and use a letter-shift code● determine whether given relationships

are functions

The study of secret codes is called cryptography.

In cryptography, encryption is the process of transforming information using an algorithm (called a cipher) to make it unreadable to anyone except those possessing special knowledge, usually referred to as a key.

The result of the process is encrypted information. The reverse process, i.e., to make the encrypted information readable again, is referred to as decryption (i.e., to make it unencrypted).

The history of cryptography began thousands of years ago.

The earliest known use of cryptography is found in non-standard hieroglyphs carved into monuments from the Old Kingdom of Egypt circa 1900 BC.

Until recent decades, it has been the story of what might be called classic cryptography — that is, of methods of encryption that use pen and paper, or perhaps simple mechanical aids.

In the early 20th century, the invention of complex mechanical machines, such as the Enigma rotor machine, provided more sophisticated and efficient means of encryption.

The introduction of electronics and computing has allowed elaborate schemes of still greater complexity, most of which are entirely unsuited to pen and paper.

The development of cryptography has been paralleled by the development of cryptanalysis — the "breaking" of codes and ciphers.

The discovery and application, early on, of frequency to the reading of encrypted communications has, on occasion, altered the course of history.

Thus the Zimmermann Telegram* triggered the United States' entry into World War I; and Allied reading of Nazi Germany's ciphers shortened World War II, in some evaluations by as much as two years.

Until the 1970s, secure cryptography was largely the preserve of governments.

Two events have since brought it squarely into the public domain:

•the creation of a public encryption standard

•the invention of public-key cryptography.

Modern encryption protects our information – especially when dealing with money – ATMs, credit cards, etc.

Input

A B C D E F G H I J K L MNO P Q R S T U V WX Y Z

Out-put

F G H I J K L MNO P Q R S T U V WX Y Z A B C D E

The table shows that the letter A is coded to the letter F, letter B is coded to G, and so on. It also shows that the letter S is coded to the letter X.

This code is called a letter-shift code. Can you see why? How would you use the code to write a message?

For this code, the letters are shifted 5 places backwards. Think of the letters A through Z as the numbers 1 through 26. How can we write a rule to represent the letter-shift code?

Input 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

Output

6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 1 2 3 4 5

You can also represent the code with a grid. Note that the input letters run across the x-axis. To code a letter, look for the shaded square directly above it. Then find the coded output by looking across to the letters that are on the y-axis. In this case, we can see that the letter O maps to the letter T. How is the shift of 5 letters revealed on the graph?

Write aShortCodedmessage.

Ex.

YWDIJHTINL YMNX

Is code for

TRYDECODIN

G THIS.

This code is called a letter-shift code. Can you see why? How would you use the code to write a message?

A RELATION is a set of ordered pairs (input/output values)

DOMAIN

The DOMAIN of a relation is the set of first coordinates of the ordered pairs.

***The X values are the DOMAIN******Input Values***

RANGE

The RANGE is the set of second coordinates.

***The Y values are the RANGE******Output Values***

Function

A FUNCTION is a relation that assigns exactly one value in the range to each value in the domain.

***Meaning X values CANNOT Repeat***

a) Domain: _______________________

b) Range:_________________________c) Is the relation a function?

Why or Why not.

_________________________

_________________________

X Y

4 3

-2 1

-1 3

4 -2

-1 1

EXAMPLE Tell whether each table represents a function. Explain why or why not.

Domain Values Range Values

Domain values “map” to its matching range value

Create a Mapping Diagram for the relation

Is the relation a function? Why or Why not.

HW 3.4