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Warm-up

Warm-up. y=3x+3 Find y if x=2. Introdcing Functions. Machines. Think of a function as a machine. You put numbers into it, the machine does something, then spits the new numbers back out. Domain and Range.

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Warm-up

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  1. Warm-up y=3x+3 Find y if x=2

  2. Introdcing Functions

  3. Machines • Think of a function as a machine. You put numbers into it, the machine does something, then spits the new numbers back out.

  4. Domain and Range • X are the numbers you put into the machine. They are called the Domain or the Input • Y are the numbers the machine puts back out. Called the Range or the Output.

  5. Example • y=x+1 • Ask: What is the machine doing? • Answer: It is adding 1 to the number put into it. • So, if I put a 1 into the machine what will I get out? • 2

  6. Example: you try • y=1.5x+3 • What is the output if the input is 5? • Answer: y=1.5(5) + 3 y=10.5

  7. Example 3 • Given the table below, list the domain and range. Domain: 1,2,3 (all the x’s) Range: -5, -7, -9 (all the y’s)

  8. Example 4: You try • Complete the table below and list the Domain and Range.

  9. How? • Simply plug in each x-value into x, and see what y is. Then, once the table is complete, the domain is all the x values, and the range is all the y values.

  10. Answer • Domain: 0,1,2,3 • Range: 1,3,5,7

  11. Graphs • How can we tell if a graph is a function? • Answer: Vertical Line Test

  12. Vertical Line Test • If you draw a vertical line ANYWHERE on the graph, and it touches the graph in more than one place, then it is not a function. • Examples on board.

  13. Homework • Worksheet 7.2 – all problems

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