0 What’s my rule? 5 Input (x) output (y) 0 5 1 What’s my rule? 6 Input (x) output (y) 0 5 1 6 What’s my rule? 2 7 Input (x) output (y) 0 5 1 2 6 7 What’s my rule? 3 ? Input (x) output (y) 0 5 1 2 3 6 7 Today, we are going to learn how to use algebraic expressions and properties to analyze numeric and geometric patterns – SPI 6.3.7 You are going to make some notations in your journals. Snoopy’s Journal My Function Machine takes a value called input and performs one or more operations on it according to a “rule” to produce a new value called the output. A function is a relation that assigns exactly one output value to one input value You can organize the input-output values of a function in a function table. Input (x) output (y) 0 1 2 3 5 6 7 8 The function rule describes the relationship between each input and output. Add 5 Input (x) output (y) 0 1 2 3 5 6 7 8 I can use an algebraic expression to represent the rule of my function machine 0 X+5 5 You can also use a “rule” to describe a pattern in a +8 sequence of numbers. For example: 8, 16, 24, 32, … A sequence is a list of numbers in a specific order. What rule would you use for the above sequence? Each number in a list is called a term of the sequence. An Arithmetic sequence can be found by adding the same number to the previous term. 8, 16, 24, 32, … +8 +8 +8 In a Geometric Sequence, each term is found by multiplying the previous term by the same number. For example: 2, 10, 50, 250, … x5 x5 x5 You can also write an algebraic expression to describe a sequence. The value of each term can be described as a function of its position in the sequence. X+5 Who uses patterns and functions? Functions are used in business to show costs. For example: Snoopytronics Inc. needs to hire a company to monitor employee computer activity. The cost is $4 per computer. If we make a table of input and output values of cost per computer, it would look like this: Input (x) output (y) 1 4 2 8 3 12 4 16 Hmmm, I wonder what the rule would be… Scientists use look for patterns when they do experiments. There are patterns in music. There are patterns in art. There are patterns in nature. Can you think of other places we find patterns? Now, let’s try some examples! What’s the rule ? Correct! Multiply by 8, or 8x What’s the missing term? Correct! 0 What’s the rule for this one? Correct! Divide by 2, x or /2 input(x) output(y) 0 7 1 9 2 11 3 13 2x + 7 Sometimes the rule can have 2 steps! Correct! 4x + 1 input(x) output(y) ? 0 1 1 5 2 9 3 13 See if you can guess the 2step rule. Now, let’s play a game to see if you can guess the rule! Now, you create a rule and matching function table and explain how you would find the input, given the rule and output values. Write it in your journal.