Question

Determine if the relation is a function.
{(0, 1), (2, 1), (3, 2), (4, 2)}

Function
Not a Function

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I don't know what a function is so please help!!

Answer 1

This is a function, due to domain are different

Answer 2

Domain is the x on the (x,y)

Answer 3

what is the domain

Answer 4

a function has only one y value for a given x value

so if at least 2 points have the same x value, but different y values .... its not a function

Answer 5

ok so all the x values are different, 0,2,3,4 so its a function.... and im guessing the domain is the x value now?

Answer 6

to see them better, stack the points vertically

(0, 1),
(2, 1),
(3, 2),
(4, 2)
^^
are any of the x values the same?

yes, the domain is conventionally the first value :)

Answer 7

spose we had another point added in: (2,3)

(0, 1),
(2, 1),
(3, 2),
(4, 2),
(2, 3)
^^
now we have 2 points with the same x value ... so we see if the y values differ or are the same

Answer 8

THANK YOU!!!, so the next question is:
(-1,3)
( 2, 4)
( 2, 5)
( 5, 6)

and this would not be a function because there are 2 x values that are the same

Answer 9

2 x values are the same AND, they each have a different y value.

Answer 10

what do the why values do?

Answer 11

each point is conventionally made of an x and y value and notated in the form: (x,y)

Answer 12

a function is a useful tool in that we can know that for a given input (x), we can expect a specific output (y).

Answer 13

can we be certain of the output (y) in this case when the input (x) is 2?

Answer 14

but does the y affect if its a function or not

Answer 15

of course

spose we define a relation as "is my girlfriend"

this is a function if and only if each boy only has one girlfriend.

lets take johnny for example: we can pinpoint johnny in the class, can we pinpoint his girlfriend? or does he have more than one girlfriend?

Answer 16

he only has one

Answer 17

lol, but, what if he has 5 girlfriends? does the output value (y) affect the situation?

Answer 18

he must be smart to get away with 5 girldriends :p and yes

Answer 19

then the answer to "does the y affect if its a function or not?" is yes.

note here that we are not stating that a girl can or cannot have more than one boyfriend :) all that matters in a function is if the boy has one and only one girlfirend.

there are different types of functions that deal with the other specifics

Answer 20

1,5
2,5
3,5
4,5

is this a function ?

Answer 21

yes...

Answer 22

correct, now why is it a function?

Answer 23

x values are the not the same

Answer 24

and the y values are

Answer 25

ok, so is this a function?

1,6
2,3
2,3
2,3
5,7

Answer 26

no, because the 3 of the x values are the same

Answer 27

that is not correct, we cannot assume that simply becasue we have multiple x values the same that it is not a function, we have to assess their y values

Answer 28

oh is it because they have the same y values to?

Answer 29

correct, IF every same x value has the SAME value .... then we are just repeating the same point over and over again. that does not change the outcome of X to Y

Answer 30

ooohhh

Answer 31

if we take the set

1,6
2,3
2,3
2,3
5,7

and weed out the redundancy (repeated point)

1,6
2,3
5,7

we see that it is in fact a function :)

Answer 32

ok so for example:
(1,-3)
(1,-3)
( 2, 5)
( 3, 8)

would be a function because you can just take out of of the (1,-3)'s.

Answer 33

correct

Answer 34

thank you!

Answer 35

your welcome, and good luck ;)

Answer 36

oh one more question

Answer 37

this would be a function right because the y values are the same, and the x values differ