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Welcome to…. FUNctions!. They are lots of ‘fun’! . So, what are functions?. Here are some ‘yes’ and ‘no’ examples of functions. . {(0,2), (1,3), (2,4), (3,5)}. {(-1,2), (-2,2), (-3,2), (-4,2)}. . {(0,2), (1,3), (1,4), (3,5)}. {(2,-2), (2,-1), (2,-2), (2,-3)}. Real definition:
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Welcome to… FUNctions! They are lots of ‘fun’!
So, what are functions? Here are some ‘yes’ and ‘no’ examples of functions.
. . . . . . . . . . . . . . . . . . . . . . . {(0,2), (1,3), (2,4), (3,5)} {(-1,2), (-2,2), (-3,2), (-4,2)} {(0,2), (1,3), (1,4), (3,5)} {(2,-2), (2,-1), (2,-2), (2,-3)}
Real definition: A relation between two variables, such that for any independent variable there is only one corresponding dependent variable value. A simpler way to think of it: A relation where each x value has only one y value. Function: By the way, all functions are relations; they’re just a more specific kind. Relation: a relationship between two variables (independent – x, dependent – y)
Relation Function y y x x y y y y
{(1,-2), (3,-4), (5,-6), (7,-8)} • {(-2,0), (-1,4), (2,8), (-2,12), (-4,14)} • c) {(-2,4), (-1,1), (0,0), (1,1), (2,4)} Identifying Functions from Ordered Pairs set notation Yes, each x-value has a different y-value. No, the x-value of –2 has more than one y-value, 0 and 12. Yes, each x-value has a different y-value. It’s okay for y-values to have multiple x-values, just not the other way around.
Identifying Functions from Graphs • vertical line test: • used to determine if a graphed relation is a function • if a vertical line crosses two or more points on a graph, then the relation is not a function • this is because at that x-value, there are two or more values for y. I am a function I am not a function
Identifying Functions from Equations a) y = 3x -1 b) x = 7 When x=1, y=2 When x=3, y=8 When x=0, y=-1 When x=-2, y=-7 • How can we tell from an equation? • picture the graph • substitute x-values Every x-value you substitute will give a different y-value. c) x2 + y2 = 16 d) y = -0.5x2 + 3x + 1 Let x=0 (easy # to work with) 02 + y2 = 16 y2 = 16 y = ±4 For each x-value you substitute, you may get two different y-values.
Types of Data One more thing… • Discrete: • based on ‘counts’ • usually whole numbers • only a finite # of values possible • values can’t be meaningfully broken into smaller units • Ex. # of people • Continuous: • Can be measured and broken into smaller parts • Can meaningfully be subdivided into smaller and smaller increments Ex. the length of a movie is 2 hours OR 1 hour and 54 minutes OR 1 hour and 54 minutes and 22 seconds OR 1 hour and 54 minutes and 22 seconds and 3 milliseconds, etc…
It’s your turn! Identify the following as discrete or continuous: Correct questions on a test Correct questions on a test Population of Brampton Population of Brampton How long you have been going out with your girl/boyfriend How long you have been going out with your girl/boyfriend Shoe size Shoe size Your weight Your weight Your age Your age Rebounds by Allen Iverson in the 2007-2008 season Rebounds by Allen Iverson in the 2007-2008 season Dwight Howard’s average rebounds per game (he beat Shaq’s record in 2007) Dwight Howard’s average rebounds per game (he beat Shaq’s record in 2007)
Makin’ it stick! 1.1 (Pg. 10) #’s 1-3, 6, 7, 8, 11
