FUNCTIONS WHAT IS A FUNCTION AND HOW DOES IT APPLY TO THE REAL WORLD

THE NUGGETIZER

DEFINITION A function is a rule that assigns every input exactly one output The inputs form a set of numbers called the domain The outputs form a set of numbers called the range Examples? –{(-2,3),(-1,2),(2,3),(1,1)} –{(-1,1), (-2,2),(-3,3),(2,5)} X-2123 Y1111

EXAMPLES Vending machines Computers Cell Phones Menus Others?

WHICH ARE FUNCTIONS? {(5,2), (7,4), (9,10), (7, 5)}{(2,3), (3,4), (5,1), (6,2), (2,4)}{(0,2), (1,3),(2,4),(3,5),(-1,1)} {(0,2), (0,3), (0,4), (0,5), (0,6)}{(10,1), (5,3), (15, 1), (5,6), (1,0)} {(1,1), (2,1), (3,1), (4,1), (5,1)} {(2,3), (3,4), (5,1), (6,2), (3,3)}{(1,1),(2,2), (3,3), (4,4), (-5,5)}{(-2,2), (3,1), (3,1), (2,4), (5,-3)} {(11, 8), (18, 17), (5, 4)} {(2,1), (2,2), (2,3), (2,4), (2,5)}{(2,3), (3,4), (5,1), (6,2), (7,3)}

GRAPHING CONTEXTS For the following context, create a graph that relates volume to time. You buy a 32oz cup at Maverick to fill at the soda machine. You begin filling the cup at a constant rate. When it is about ¾ full, you wait for the foam to settle, then fill it some more. You repeat this two more times until the cup is just about full. Then you put a lid on it and drink it. You drink quickly at first, then slow down and sip on the cup for awhile until it’s empty. Time Volume

WHAT CAN WE LEARN FROM A GRAPH Inputs/Outputs: –What is the height of the ball at 1s? 1.5s? –At what times was the ball 0.6m off the ground? Change: –When was the ball going up? Speed: –When was the ball moving the fastest? Graph of the height of a basketball in meters compared to time in seconds

WHAT CAN WE LEARN FROM A GRAPH How far up the hill was the bicyclist after 4 minutes? How long did it take the bicyclist to reach the top of the hill? How long did it take the bicyclist to get down the hill? When was the bicyclist going the fastest? When was the bicyclist going the slowest? Did the bicyclist ever take a break? How do you know? Graph of the position bicyclist in relation to bottom of the hill over time time (min) position (m)

VERTICAL LINE TEST Is this a function? –How do you know? If a vertical line touches the graph of an equation more than once, it doesn’t represent a function

PRACTICE THE VERTICAL LINE TEST Which of the following are functions?

INPUT / OUTPUT TABLES Complete the table using the graph at the right XY

INPUT / OUTPUT TABLES Complete the table using the graph at the right XY

CONTEXTS RELATED TO GRAPHS Create an input/output table for the graph to the right. Create a context (story) that matches the given graph X Y