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Functions and Rules (Example 1) 7 5 5 7 23 3 27 39 11 19 35 15 15 8 20 17 23 9 23 32 11 13 21 11 17 29 14 Output Output Output 5n + 3 6n - 1 13 33 8 38 53 18 28 48 23 2 6 1 7 10 3 5 9 4 11 35 5 41 59 17 29 53 23 Output INPUT Output

Functions and Rules (Example 2) 3 -5 1 10 -2 7 51 15 42 69 96 60 24 33 78 7 13 5 16 25 13 -3 -1 9 1 4 19 Output Output Output n2 + 1 n2 - 3 26 2 17 5 1 4 7 10 6 2 3 8 22 -2 13 46 97 33 1 6 61 50 101 37 5 10 65 Output INPUT Output

Functions and Rules (Example 3) 9 3 51 11 2 19 7 103 199 403 147 39 67 259 74 99 201 73 146 299 107 26 47 191 19 33 129 Output Output Output n2 + n n2 – 2n 6 2 30 2 1 5 7 10 6 3 4 8 -1 15 35 80 24 3 8 48 56 110 42 12 20 72 Output INPUT Output

Functions and Rules (Example 1) 2 6 1 7 10 3 5 9 4 2n + 3 3n + 2 4n - 1 5n + 3 6n - 1 INPUT Output

Functions and Rules (Example 2) 5 1 4 7 10 6 2 3 8 2n - 7 3n - 5 9n + 6 n2 + 1 n2 - 3 INPUT Output

Functions and Rules (Example 3) 2 1 5 7 10 6 3 4 8 2n2 + 1 3n2 - 1 4n2 + 3 n2 + n n2 – 2n INPUT Output

Functions and Rules (1a) 6 2 5 10 3 7 9 4 n + 5 2n + 3 3n - 4 5n + 1 6n - 3 INPUT Output

Functions and Rules (1b) 7 9 4 5 10 2 6 3 1 2n + 5 3n + 1 4n - 3 6n + 1 8n - 3 INPUT Output

Functions and Rules (1c) 7 9 4 5 10 2 6 3 1 3n + 5 4n + 1 5n - 3 6n + 9 9n - 1 INPUT Output

Functions and Rules (2a) 4 1 5 8 10 6 2 3 7 n - 3 2n - 5 4n + 6 n2 + 3 n2 - 2 INPUT Output

Functions and Rules (2b) 5 1 4 6 10 8 2 7 3 2n - 3 3n - 7 4n + 5 n2 + 8 n2 - 5 INPUT Output

Functions and Rules (2c) 8 1 2 6 10 5 4 7 3 3n - 3 4n - 7 5n + 3 n2 + 9 n2 - 7 INPUT Output

Functions and Rules (3a) 2 1 5 7 10 6 3 4 8 2n2 + 1 3n2 - 2 4n2 + 5 n2 - n n2 – 3n INPUT Output

Functions and Rules (3b) 2 1 5 7 10 6 3 4 8 3n2 + 2 4n2 - 1 5n2 + 7 n2 – 3n n3 – n2 INPUT Output

Functions and Rules (3c) 2 1 5 7 10 6 3 4 8 3n2 + 7 5n2 - 3 6n2 + 9 n2 – 4n n3 – 2n2 INPUT Output