Relations and Functions

1. Relations and Functions Unit 3-3 Sec. 3.1

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

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

5. Example 3: Domain: {1, 2, 3} 1 2 3 Range: {2}

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

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

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

10. Function? Example 2: NO!

11. Vertical Line Test

12. Function? YES! NO!

13. Your Turn YES! NO!

14. 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. Evaluating Functions Evaluate f(-2).

16. Evaluating Functions Evaluate f(1) and f(a)

17. Your Turn Evaluate f(3).

18. Evaluating Functions on a Graph f(0) = f(1/2) = f(-2) = 3 0 4

19. Assignment • P. 229 • #15-25 odd, and 27 a, b, c • DUE: TOMORROW!