Functions TEXTBOOK REFERENCE: 4-6

What is a relation? All ordered pairs are relations! A relation is any set of ordered pairs. {(3,4), (4,5), (5,6)} {(3,4), (3,5), (3,6)} Each number in the set of ordered pairs is called an element. All ordered pairs are relations!

All x coordinates are different numbers = function! What is a function? A function is a relation in which only one x matches with a y Relation and Function {(3,4), (4,5), (5,6)} Relation only {(3,4), (3,5), (4,6)} All x coordinates are different numbers = function!

Functions as Ordered Pairs {(4,5), (-1, 0), (3,0)} All x are different, y does not matter!

Functions as Tables {(4,5), (-1, 0), (3,0)} x y -1 3 4 5

Functions as Graphs A graph that is a function must pass the vertical line test Which of the graphs below represents a function? Place your pencil vertically on the graph! If your pencil touches the picture only once, you have a function! Function

Function Parts A function is a relationship where on thing depends upon another. A function has three parts: Input – x (plug in number) Function Rule– problem (arithmetic or geometric sequence) Output – y (answer)

Making Function Tables A function table organizes your work so you can find out what the ordered pairs are. Input x Function Rule 5x Output y Ordered Pairs* (x, y) 1 5 x 1 5 (1, 5) 2 5 x 2 10 (2, 10) 3 5 x 3 15 (3, 15) 4 5 x 4 20 (4, 20)

Making Function Graphs A function graphs plots the ordered pairs you found on the coordinate plane Input x Function Rule 2x Output y Ordered Pairs* (x, y) 1 2 x 1 2 (1, 2) 2 x 2 4 (2, 4) 3 2 x 3 6 (3, 6) 2 x 4 8 (4, 8)

Real World Function Graphs Chuck earns $4 an hour cleaning his room. Create table and graph to represent this situation. Input X hours Function Rule 4x $4 x hours Output Y Pay $ Ordered Pairs* (x, y) 1 4 x 1 hour $4 (1, 4) 2 4 x 2 hours $8 (2, 8) 3 4 x 3 hours $12 (3, 12) 4 4 x 4 hours $16 (4, 16)

What are Linear Equations? A linear equation is an equation that forms a a straight line when graphed. y = 2x + 1 y is output although listed first. X = the input.

Steps for Graphing Linear Equations Create a four-column function table. Select any four values or numbers to substitute for the input x (I suggest -1, 0, 1, 2) Perform rule. Write output. List ordered pairs. Graph on Coordinate Plane.

Steps for Graphing Linear Equations, cont’d. x 2x+1 y (x, y) 2 2(2)+1 5 (2, 5) 1 2(1)+1 3 (1, 3) 2(0)+1 (0, 1) -1 2(-1)+1 (-1, -1)

Steps for Graphing Linear Equations, cont’d. Every point on the line is a solution to y =2x +1.