Understanding Functions Through Graphs and Coordinates

1. Monday, September 30th Please Complete Warm Up Warm-Up September 27th Solve and graph -10 < 2x – 5 ≥ 12 Solve for L: m=2∏²-2∏L

2. Functions vs Relations

3. Coordinate Plane: Graph formed by the intersection of 2 number lines (axes) Origin: The point of intersection; (0,0) X-axis: Horizontal Number Line Y-axis: Vertical Number Line Ordered Pair: Points on a graph (x-coordinate, y-coordinate) Vocabulary

4. Quadrants

5. X coordinate: Tells me how many units to move left of right Negative: left Positive: right Y Coordinate: Tells me how many units to move up or down Negative: down Positive: up Do you Remember How to Graph?!?!?!? Graph A: (3,5)B: (-2, 4)C: (3,-6)

6. •F •E •G •H Name that Quadrant! y 1. E Quadrant ll 2. F no quadrant (y-axis) x 3. G Quadrant l 4. H Quadrant lll

7. 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 What is a Function? Input Output y= 10x + 5

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

9. 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

10. 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)

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

12. Function • A relation 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.

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

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

15. How can I remember Domain and Range?

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

17. 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

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

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

20. Function or relation? Example 2: function

21. Function or relation? Example 3: relation

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

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

24. Function or Relation? relation

25. Function Notation

26. Function form of an equation • A way to name a function • f(x) is a fancy way of writing “y” in an equation. • Pronounced“f of x”

27. Evaluating Functions

28. Tell me what you get when x is -2. Evaluating a function f(x) = 2x – 3 when x = -2 f(-2) = 2(-2) – 3 f(-2) = - 4 – 3 f(-2) = - 7

29. Tell me what you get when x is -3. Evaluating a function f(x) = x2 – 2x + 3 find f(-3) f(-3) = (-3)2 – 2(-3) + 3 f(-3) = 9 + 6 + 3 f(-3) = 18

30. Domain and Range Only list repeats once Put in order from least to greatest

31. What are the Domain and Range? {1, 2, 3, 4, 5, 6} Domain: Range: {1, 3, 6, 10, 15, 21}

32. What are the Domain and Range? Domain: Range: {0, 1, 2, 3, 4} {1, 2, 4, 8, 16}

33. 15. What are the Domain and Range? Domain: Range: x ≥ -1 All Real Numbers

34. Homework/Classwork Function Practice Worksheet