1. 9/8/2015 1 Relations and Functions Unit 3-3 Sec. 3.1

2. 2 9/8/2015 Definitions: Relations – a set of ordered pairs Domain – the set of all possible input values of a relation or function. (x-values, input, independent variables). Range – the set of all possible output values of a relation or function. (y-values, output, dependent variables).

3. 3 9/8/2015 Identifying the Domain & Range {(100, 5), (120, 5 ), (140, 6 ), (160, 6), (180, 12)} Example 1: Domain: Range: List Domain and Range in increasing order!!! {5, 6, 12} {100, 120, 140, 160, 180}

4. 4 9/8/2015 Identify the Domain & Range Example 2: Domain: Range: {3, 5, 7} {-1, 0, 9} The arrow leaves the input values (x) and points at the output values (y).

5. 5 9/8/2015 Example 3: Domain: {1, 2, 3} Range: {2} 123123

6. 6 9/8/2015 Identify the Domain & Range Example 4: List the x-values for Domain and the y-values for Range Domain: Range: { } -2,-1,0,1,2,3 { } -3,-2,-1, 0,1,2

7. 7 9/8/2015 Definition Function – a relation in which every input is paired with exactly one output. - For every x, there is one y - 2 inputs can have the same output, but an input cannot have 2 outputs.

8. 8 9/8/2015 Function or Not a Function? Function – a relation in which every input is paired with exactly one output. Function? NO!YES!

9. 9 9/8/2015 Function? {(100, 5), (120, 5 ), (140, 6 ), (160, 6), (180, 12)} Example 1: YES!

10. 10 9/8/2015 Function? Example 2: NO!

11. 11 9/8/2015 Vertical Line Test

12. 12 9/8/2015 Function? YES!NO!

13. 13 9/8/2015 Your Turn YES!NO!

14. 14 9/8/2015 Function Notation If x is the independent variable and y is the dependent variable, then the function notation for y is f(x), read “ f of x ” where f names the function. Ex. y = 2x f(x) = 2x

15. 15 9/8/2015 Evaluating Functions Evaluate f(-2).

16. 16 9/8/2015 Evaluating Functions Evaluate f(1) and f(a)

17. 17 9/8/2015 Your Turn Evaluate f(3).

18. 18 9/8/2015 Evaluating Functions on a Graph f(0) = f(1/2) = f(-2) = 304

19. Assignment P. 229  #15-25 odd, and 27 a, b, c  DUE: TOMORROW! 19 9/8/2015