The document discusses functions and how to determine if a relation is a function. It defines a function as a relation where there is exactly one output for every input. It introduces the vertical line test as a way to recognize functions - if a vertical line can only intersect the graph of a relation at most once, it is a function.

1. Objective - To recognize whether a relation is a function and to use function notation Relation - Any set of ordered pairs Function - A type of relation where there is exactly one output for every input. For every x there is exactly one y. Not a Function Function x y 1 2 6 7 x y 1 2 6 7

2. y x -2 -1 0 1 2 -4 -2 0 2 4 y = 2x input output -2 -1 -4 -2 0 1 0 2 2 4 x-y chart mapping Function

3. y x -2 -1 0 1 2 2 1 0 1 2 y x -2 -1 0 1 2 2 1 0 1 2 Determine whether the equation is a function. input output -2 -1 0 1 0 1 2 2 input output 0 1 2 -2 -1 0 1 2 Not a Function Function

4. Vertical Line Test - Functions x y x y x y x y x y x y x y x y Function

5. Vertical Line Test - Functions x y x y x y x y x y x y x y x y Function Function

6. Vertical Line Test - Functions x y x y x y x y x y x y x y x y Function Function Not a Function

7. Vertical Line Test - Functions x y x y x y x y x y x y x y x y Function Function Not a Function Function

8. Vertical Line Test - Functions x y x y x y x y x y x y x y x y Function Function Not a Function Function Not a Function Function Not a Function Not a Function

9. Tell whether the relation below is a function. 1) 2) 3) 4) input output 0 1 5 2 3 y x -3 -3 -3 -3 -1 0 1 2 x y Function Not a Function Not a Function input output -2 -1 0 3 4 5 6 Not a Function

10. Function Notation

11. Evaluate the following.

12. Evaluate the function over the domain, x = -1, x = 0, x = 2.

13. Graph the linear function. x -3 -2 -1 0 1 2 3 6 5 4 3 2 1 0 x y