Functions and Relations OBJECTIVE Determine whether a relation

Functions and Relations

OBJECTIVE Determine whether a relation is a function or not a function.

ESSENTIAL QUESTION How do we determine if a relation is a function or not?

Definitions 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.

x 1 2 y 6 7 Not a Function x 1 2 y 6 7 Function

y = 2 x x-y chart mapping xy input output -2 -4 -1 -2 00 12 24 -2 -1 0 1 2 -4 -2 0 2 4 Function

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

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

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

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

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

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

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

Function Notation

Evaluate the following.

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

Graph the linear function. f(x) x -3 -2 -1 0 1 2 3 6 5 4 3 2 1 0 x