1. Algebra 1 Unit 4

2. GRAPHING STORIES: Watch the videos on the next two slides and graph the story.

3. GRAPHING STORIES: Watch the video and graph the story. Clock: www.graphingstories.com/2kj www.graphingstories.com/2kj

4. GRAPHING STORIES: Watch the video and graph the story. Height of waist off ground: www.graphingstories.com/4my www.graphingstories.com/4my

5. 5x2x2 25 How would you use your calculator to solve 5 2 ? The number you entered is the input number (or x-value on a graph). The result is the output number (or y- value on a graph). The x 2 key illustrates the idea of a function. InputOutput Press:

6. A function is a relation that gives a single output number for every valid input number. There are many ways to represent relations: A relation is a rule that produces one or more output numbers for every valid input number. These are all ways of showing a relationship between two variables. Graph Equation Table of values A set of ordered pairs Mapping

7. A function is a rule that gives a single output number for every valid input number. To help remember & understand the definition: Think of your input number, usually your x-coordinate, as a letter. Think of your output number, usually your y-coordinate, as a mailbox.

8. A function is a rule that gives a single output number for every valid input number. Input number Output number Can you have one letter going to two different mail boxes? Not a FUNCTION

9. A function is a rule that gives a single output number for every valid input number. Input number Output number Can you have two different letters going to one mail box?

10. Are these relations or functions? xy x y 1515 2626 3737 4646 12341234 567567 Function & Relation

11. Are these relations or functions? xy x y 1515 2626 17 16 1212 567567 Not a Function but a Relation

12. xy x y 1515 2626 211 3838 123123 5 6 8 11 Not a function But a relation Are these relations or functions?

13. x y -2 1 0 3 1 5 Double the number and add 3 As an equation: In words: y = 2x + 3 As a table of values: As a set of ordered pairs: (-2, -1) (-1,1) (0,3) (1, 5) (2, 7) (3, 9) These all represent the SAME function!

14. 56 45 32 43 51 YX We know it is a function because non of the “x” values in the table repeat. We can also hold a vertical line up to the points and see that no 2 points are touched by the same vertical line This method of determining a function from a graph is know as the vertical line test

15. #1 -22 -31 -40 -5 -6-2 YX Is this a function? Run vertical line across the graph and see if it touches two places at the same time This is a function because it passes the vertical line test.

16. 54 41 32 43 51 YX #2 Notice the two points that are touched by the green line. This means that the relation is not a function

18. Functional Notation An equation that is a function may be expressed using functional notation. The notation f(x) (read “f of (x)”) represents the variable y.

19. 1. For the function f(x) = 2x + 6, the notation f(3) means that the variable x is replaced with the value of 3. f(x) = 2x + 6 f(3) = 2(3) + 6 f(3) = 12 Functional Notation Con’t (3, 12)

20. Given f(x) = 4x + 8, find each: f(2) 2. Evaluating Functions = 4(2) + 8 = 16 (2, 16)

21. If f(x) = 3x  1, and g(x) = 5x + 3, find each: Evaluating More Functions = [3x - 1] + [5x + 3] = 3x – 1 + 5x + 3 = 8x + 2 = [3x - 1] - [5x + 3] = 3x – 1 – 5x - 3 = -2x - 4 1. f(x) + g(x) 2. f(x) - g(x)