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This is a function, due to domain are different
Domain is the x on the (x,y)
what is the domain
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
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?
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 :)
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
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
2 x values are the same AND, they each have a different y value.
what do the why values do?
each point is conventionally made of an x and y value and notated in the form: (x,y)
a function is a useful tool in that we can know that for a given input (x), we can expect a specific output (y).
can we be certain of the output (y) in this case when the input (x) is 2?
but does the y affect if its a function or not
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?
he only has one
lol, but, what if he has 5 girlfriends? does the output value (y) affect the situation?
he must be smart to get away with 5 girldriends :p and yes
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
1,5 2,5 3,5 4,5 is this a function ?
correct, now why is it a function?
x values are the not the same
and the y values are
ok, so is this a function? 1,6 2,3 2,3 2,3 5,7
no, because the 3 of the x values are the same
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
oh is it because they have the same y values to?
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
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 :)
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.
your welcome, and good luck ;)
oh one more question
|dw:1370354253440:dw| this would be a function right because the y values are the same, and the x values differ