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Trick or Treat Halloween was almost over, and Mr. Green had less than 20 candies left. When the doorbell rang, he thought he would give all the candies away. When he opened the door, there were two trick or treaters. He wanted to give away the candies evenly, but he noticed that when he divided the candies in two, there was one left over. At that point, he saw another trick or treater behind the first two. He tried to divide the candies evenly among the three of them, but again one was left over. Finally, another trick or treater came to his door, making it four trick or treaters altogether. Mr. Green still had one candy left over after dividing the left over candies in fours. How many candies did Mr. Green have left when the doorbell rang?

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**Trick or Treat Solution**

Mr. Green had 13 candies left over. 13 is the only number under 20 that fits the description (it is one more than 12, which is evenly divisible by 2, 3, and 4).

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**Functions and Linear Equations**

Lesson 4-6

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**Function A relationship where one thing depends on another.**

In a function you start with an input number, perform an operation, and get an output number. FUNCTION RULE INPUT OUTPUT

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Function Table You can organize the input numbers, output numbers, and function rule in a function table. Lets Try an example

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Example Suppose you earn $5 each week. Make a function table to show your total earnings after 4 weeks. Input (# of weeks) Function rule ( x 5) Output (total earnings) 1 5 x 1 5 2 5 x 2 10 3 5 x 3 15 4 5 x 4 20

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**Words to Know Domain= the input values Range= the output values**

In our example the domain would be written as { 1, 2, 3, 4 } and the range would be written as { 5, 10, 15, 20 } The domain or input represents the x value and the range the y value. Together they form an ordered pair.

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Example Function rule Input Output Make a function table and graph the equation. y = x -3 Domain = {1,0,-1,-2} Range = {-2,-3,-4,-5} Ordered pairs = (1, -2) (0, -3) (-1,-4) (-2, -5) x X-3 y 1 1 - 3 -2 0 - 3 -3 -1 - 3 -1 -4 -2 -2 - 3 -5

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Example Function rule Input Output Make a function table and graph the equation. y = 2x Domain = {1,2,3,4} Range = {2,4,6,8} Ordered pairs = (1, 2) (2, 4) (3,6) (4, 8) x 2x y 1 2(1) 2 2 2(2) 4 2(3) 3 6 4 2(4) 8

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Example Function rule Input Output Make a function table and graph the equation. y = 2x -1 Domain = {1,2,3,4} Range = {1,3,5,7} Ordered pairs = (1, 1) (2, 3) (3,5) (4, 7) x 2x -1 y 1 2(1)-1 1 2 2(2)-1 3 2(3)-1 3 5 4 2(4)-1 7

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Your Turn Make a function table and graph the equation. y = -3x

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**Homework Complete Lesson 4-6 # 2-14 evens**

Test Friday, Lessons 4-5 and 4-6. Begin Studying and Practicing Now!

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Domain: a set of first elements in a relation (all of the x values). These are also called the independent variable. Range: The second elements in a relation.

Domain: a set of first elements in a relation (all of the x values). These are also called the independent variable. Range: The second elements in a relation.

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