1. Ch. 12.1 Relations and Functions Objective: To be able to determine whether a given relation is a function.

2. InputOutputFunction xy 210 315 420 735y = 5x...... InputOutput xy 210 315 420 525 630 735 y = 5x Function – a relation where there is exactly one y (range) for every x (domain).

4. A rule or equation where there is exactly one output for every input. Function - For every x-value there is exactly one y-value. x 0 1 2 4 y -2 0 2 4 6 No x- value repeats Yes, it is a function x 0 1 2 4 y 2 0 2 4 6 No x- value repeats Yes, it is a function x 1 0 1 2 4 y -2 0 2 4 6 x-value repeats No, it is not a function 1 2 -2 2 1

5. Write a function rule that relates x and y in the tables below. 1) 2) 3) 4) x -2 -1 0 1 2 3 y -8 -4 0 4 8 12 y = 4x x -2 -1 0 1 2 3 y 3 4 5 6 7 8 y = x + 5 x -2 -1 0 1 2 3 y y -4 -1 2 5 8 11 y = 3x + 2

6. Examples: Determine whether each relation is a function Domain Range 110 220 330 440 Yes, its is a function. Domain Range 49 918 510 112 Yes, it is a function.

7. Examples: Determine whether each relation is a function Domain Range 6 36 3 -410 911 2112 -9 Yes, it is a function. Domain Range 1414 103 2929 1515 No, it is not a function.

8. Example Find the domain and range of each relation. Is the relation a function? 1.[(3,6), (7,1), (4,21), (9,100)] 2. [(15, 2), (15,1), (2,9), (2, 11)] 3. [(1,1), (2,2), (3,3), (4,4)]