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Wednesday, October 16 th Please complete the warm up 

Wednesday, October 16 th Please complete the warm up . Blast From the Past 1. What is the constant in the expression 2 . The product of 8 and the sum of a number and 4 is greater than 10 . Unit 3: Functions Linear vs. Exponential. What is a Function? . Input. Output. y = 10 x + 5.

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Wednesday, October 16 th Please complete the warm up 

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  1. Wednesday, October 16th Please complete the warm up  Blast From the Past 1. What is the constant in the expression 2. The product of 8 and the sum of a number and 4 is greater than 10.

  2. Unit 3:FunctionsLinear vs. Exponential

  3. What is a Function? Input Output y= 10x + 5 It’s like a machine! You INPUT a number to get an OUTPUT Input: The value substituted for x Output: The value generated to get y

  4. Let’s think About it…… Input Input: 5 Output:____ Input: -2 Output:___ Input: 6 Output:____ Y = 3x Out put

  5. Engraver’s fee is $10 plus word $2 for each y 10 x = + 2 · Real World Application An engraver charges a setup fee of $10 plus $2 for every word engraved. Write a rule for the engraver’s fee. Write ordered pairs for the engraver’s fee when there are 5, 10, 15, and 20 words engraved. Let y represent the engraver’s fee and x represent the number of words engraved. y = 10 + 2x

  6. Organizing it All 5 y = 10 + 2(5) 20 (5, 20) 10 30 (10, 30) y = 10 + 2(10) y = 10 + 2(15) 15 (15, 40) 40 20 50 y = 10 + 2(20) (20, 50)

  7. Relation • Any set of input that has an output • Input and output values are ordered

  8. Function • A relation is where EACH input has exactly ONE output • Each element from the domain is paired with one and only one element from the range • Different input values can have the same output value.

  9. Domain • x – coordinates • Independent variable • Input

  10. Range • y – coordinates • Dependent variable • Output

  11. How can I remember Domain and Range?

  12. NOTICE X comes before Y & D (Domain) comes before R (Range) X’s=Domain Y’s= Range

  13. How do I know it’s a function? • Look at the input and output table – Each input must have exactly one output. • Look at the Graph – The Vertical Line test: NO vertical line can pass through two or more points on the graph

  14. Vertical Line Test Vertical Line Test: 1. 2. 3.

  15. Function or relation? Example 1: {(3, 2), (4, 3), (5, 4), (6, 5)} function

  16. Function or relation? Example 2: function

  17. Function or relation? Example 3: relation

  18. Function or relation? Example 4: ( x, y) = (student’s name, shirt color) function

  19. Function or relation? Example 5: Red Graph relation

  20. Function or Relation? relation

  21. Comic Strip Helpful Reminders • Do you have your system listed Example: y=4x + 5 and y=3x -3 2. Did you solve your system in one of the three methods: elimination, substitution, graphing • Is it neatly written? • Do you have AT LEAST 6 slides? Due Wednesday at end of class

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