- shelby1290

Determine whether the following relations are functions. Give the appropriate reason for your answer. *pictures included
a) {1,3), (2,3), (3,2), (1,4), (4,1)}
b) picture
c)picture
d)picture
e)picture

- chestercat

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- shelby1290

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- shelby1290

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- anonymous

if you want to know that a relation is function look at the x of every ordered pair.if you saw that one of x is repeated and their y isn't same that relation isn't a function for example : {(1,2),(1,3)} is not a function.

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- anonymous

for b
do two arrows come out of any number?

- anonymous

and for d and e we use a test :vertical line test
If a vertical line can be drawn that crosses two points on the graph of the relation, then the relation is not a function.

- shelby1290

@amirreza1870 i see...but what if your x values aren't the same but one of y-values is repeated twice? Is that a function?

- shelby1290

|dw:1442369545961:dw|

- shelby1290

^like that for example

- misty1212

HI!!

- shelby1290

@satellite73 no they don't. Does that make it a function or not a function? How about part c?

- misty1212

y values are unimportant for determining if it is a function or not

- shelby1290

then what must I pay attention to?

- anonymous

since there is only one arrow out of each domain element, then it IS a function

- shelby1290

I always get confused when it comes to identifying them

- misty1212

only pay attention to the x values
if they are repeated, it is NOT a function

- anonymous

no a is a function but it is not one-to-one

- misty1212

don't fret about "one to one" yet, worry about that later

- shelby1290

@amirreza1870 what's one-to-one ?

- misty1212

vertical|dw:1442369892767:dw| line test is easy if you have a graph

- anonymous

i an sorry about using one-to -one but that means a function that for every x ,y is a different number for example {(1,3),(2,3)} is function because 1 and 2 are different but it's not one-to-one because their y is same.

- shelby1290

@misty1212 so part d is a function because it passes the vertical line test and doesn't go through more than one point? and part e) is not a function because it failed the vertical line test and passes through more than one point

- shelby1290

@amirreza1870 okay i get that so if the x-values are different its referred to as one-to-one ?

- anonymous

no. if the y values are different it is a one-to-one function.the difference of x values show that relation is function

- shelby1290

ahhhh okay so...
one-to-one=not a function
difference in x-values=function

- anonymous

we use this expression (one-to-one) for a function. so a relation must be a function if we want to see that is one-to-one or not

- anonymous

i think it's better to use a Venn diagram |dw:1442371114951:dw|
as you can see only one arrow comes out of a and b so this is a function but their y is same (we said if the y was different it is one-to-one) so it is not one-to-one

- shelby1290

alright that makes sense
thanks for the help!

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