4.8 Functions and Relations Goal: Decide whether a relation is a function and use function notation

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.

One input gives 2 outputs Vocab Function = A set of ordered pairs that has each input (x) giving exactly one output (y) Ex: Function or not? In a function, one input can’t give 2 different outputs! X Y -2 3 4 8 32 7 5 X Y 5 3 4 8 32 -6 X Y -2 3 -1 8 7 Yes No; One input gives 2 outputs Yes

More Vocab (x, y) = (input, output) f(x) is another way to write an output Domain = the set of all inputs (x) Range = the set of all outputs (y) Ex: For the function f(x) = x – 3 , evaluate the following: f(-3) f(x+1)

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

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

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

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

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

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

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

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

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

Discrete vs. Continuous Discrete relation: A relation where the domain is a set of individual points Continuous relation: A relation that can be graphed with a line or smooth curve