218 Chapter 2 Linear Equations in Two Variables and Functions Group Activity Deciphering a Coded Message Materials: A calculator Estimated time: 20–25 minutes Group Size: 4 (two pairs) Cryptography is the study of coding and decoding messages. One type of coding process assigns a number to each letter of the alphabet and to the space character. For example: A B C D E F G H I J K L M N 1 2 3 4 5 6 7 8 9 10 11 12 13 14 O P Q R S T U V W X Y Z space 15 16 17 18 19 20 21 22 23 24 25 26 27 According to the numbers assigned to each letter, the message “Decimals have a point” would be coded as follows: D E C I M A L S __ H A V E __ A __ P O I N T 4 5 3 9 13 1 12 19 27 8 1 22 5 27 1 27 16 15 9 14 20 Now suppose each letter is encoded by applying a function such as f(x) 2x 5, where x is the numerical value of each letter. For example: The letter “a” would be coded as: f(1) 2(1) 5 7 The letter “b” would be coded as: f(2) 2(2) 5 9 Using this encoding function, we have Message: D E C I M A L S __ H A V E __ A __ P O I N T Original: 4 5 3 9 13 1 12 19 27 8 1 22 5 27 1 27 16 15 9 14 20 Coded Form: 13 15 11 23 31 7 29 43 59 21 7 49 15 59 7 59 37 35 23 33 45 To decode this message, the receiver would need to reverse the operations assigned by f(x) 2x + 5. Since the function f multiplies x by 2 and then adds 5, we can reverse this process by subtracting 5 and dividing by 2. This is represented by g1x2 x 5 2 . 1. a. One pair of students will encode the follow message according to MATH IS THE KEY TO THE SCIENCES f1x2 4x 2. b. The second pair of students will encode the follow message according to MATH IS NOT A SPECTATOR SPORT f1x2 3x 1. 2. With each message encoded, the pairs will exchange papers. Each pair will then decode the message.
miller_intermediate_algebra_4e_ch1_3
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