Functions

What is a Function Relation- a set of ordered pairs (0,3) ( 2,4) ( 4, 5) ( 0,2) ( 0, 3) ( 0, 5)

What is a Function Function a very special type of relation Its like a Coke machine You hit coke, you only get coke, you hit sprite, you get sprite Function- for every one input, there is only one output

Examples ( 1,4) ( 2, 5) ( 3,7) ( 3,4) ( 6,9) ( 10,12) The x’s do not repeat Every function is a relation, but not every relation is a function

Function Basics Inputs (x’s) cannot repeat Outputs(y’s) can repeat Sometimes there are more than one button for a coke on the coke machine ( 1,2) ( 1,3) ( 1,4) NOT A FUNCTION ( 1,1) ( 2,1) ( 3,1) Is a Function

Domain and Range Domain- Input values of the Function X numbers Range- Output values of the Function, y numbers Domain- Coke Button Diet Coke Button, Sprite Button Range- Coke, Diet Coke, Sprite

Graphs A function has only one y value for every x value So it cannot be a function, if a graph has pts with the same x value

Vertical Line Test To determine if a line on a graph is a function If you can draw a vertical line anywhere on a graph and it insects the graph in more than one place, it is not a function

Examples

Functional Notation F(x) means the function of x So instead of writing y= 2x + 3 F(x) = 2x + 3 So F(2) = 7 F(3) = 9