Question

medal medal medal please help
The tables below show the values of y corresponding to different values of x:


Table A
x 3 3 2
y 1 0 0
Table B
x 3 5 5
y -2 2 -2


Which statement is true for the tables?
Both Table A and Table B represent functions.
Both Table A and Table B do not represent functions.
Table A does not represent a function but Table B represents a function.
Table A represents a function but Table B does not represent a function.

Answer 1

@mathmate @mathmath333 please help

Answer 2

do you think you can help

Answer 3

When the question arises whether a relation (table, diagram, graph, etc) is a function, it suffices to check that f(x) is UNIQUELY defined for any value of x.

Answer 4

A function is a relation in where every input has exactly one output, so which ones are functions? @ro561man

Answer 5

I dont know what you mean every input has exactly one output

Answer 6

For example,

in the above drawing, f(x) is a function, because no matter what value of x we choose, we can only find one value of f(x).
g(x) is not a function, because for at least one value of x, we can find two values of g(x), so g(x) is not UNIQUELY defined at that point.
You can apply the same principle to the given tables A and B.

Answer 7

By "every input has exactly one output", @AnswerMyQuestions means for each value of x, there is a unique (one and only one) value of y. In math, we often say "exactly one" meaning no more and no less than one.
If you look at the drawing I made, I hope it helps you visualize the situation.
Example:
Table P
x y
1 2
2 3
1 1
Table Q
1 2
2 3
3 2
Table P is not a function, because for x=1, we cannot say y=2 or y=1, so f(1) is not unique.
Table Q is a function, because for every value of x, we have a single value of y.

Answer 8

@mathmate Iam sorry my computer shut down may you please help me

Answer 9

The question above, or a new one?

Answer 10

Above ofc. :P

Answer 11

He never got his answer. :P

Answer 12

same question above thanks for coming

Answer 13

can you still see the answers above (that we see)?

Answer 14

the graph and other things

Answer 15

yes

Answer 16

ok. Do the answers make sense to you?

Answer 17

I mean some of it yes like the part where you said you only get one answer for y

Answer 18

That is the best way to see if a relation is a function.
If you find a single case where y could take two values for the same x, then it is not a function.

Answer 19

Yes, you can only have different y-values for the tables to be functions. The y-values can't be the same number, or the table isn't a function.

Answer 20

So which are tables, and which are not?

Answer 21

oh ok so what would it be if it weren't a function and would the answer be D

Answer 22

@mathmate r u there

Answer 23

No... That's incorrect...

Answer 24

Which tables have the same y-values?

Answer 25

yes, depends if both A & B are non-functions.

Answer 26

So the answer is B right

Answer 27

It helps if you focus on your answer before the choices!
Which of the tables are functions and which are not?

Answer 28

Why would you choose B?

Answer 29

I don't think either of them are because Table A has 2 0's and Table B has 2 -2's

Answer 30

Yes, you conclusion is correct, so you can go ahead and make your choice.
I have one more comment to make later.

Answer 31

what is it

Answer 32

I'll let you make your choice first, the comment is a general comment.

Answer 33

Im going with B

Answer 34

That's correct! good job!

Answer 35

Now the comment.

Answer 36

Remember I mentioned the "unique value test"?

Answer 37

yeah

Answer 38

What is important is that for a given value of x, you only have one (or the same) value of y.

Answer 39

so far so good?

Answer 40

yeah

Answer 41

ok, it is important to remember that because if I give you the following table, tell me if it is a function:
x y
1 3
3 5
4 3
1 3
Is this a function?

Answer 42

no it's not

Answer 43

This was a trap! It IS a function! Explain to me!

Answer 44

Explain why it is, or why it is not, please!

Answer 45

It isn't because there are 2 1,3's

Answer 46

The x-values don't matter. It's just the y-values. @ro561man

Answer 47

Many people would go by count of the number of x-values, whenever the x-values repeat, they would conclude that it is not a function. This works most of the time because in a set, we are not allowed to duplicate ordered pairs.
However, the real criterion is the question what is the value of f(1).
If f(1) equals 3 in both cases, it is stilll a unique value!

Answer 48

in that case there are 3 3's

Answer 49

If and when the x values repeat, check the values of y, if they are the same, it's ok.
What we need is for every value of x, we get the SAME and UNIQUE y value.
Numbers don't count.

Answer 50

??? you lost me what grade r u in

Answer 51

What I am saying is many students are taught to count the number of x-values, and were told that x-values cannot repeat.
This is true only if the corresponding y-values are different, so that we cannot find a unique value for y.
I'll explain using our example:
x y
1 3
3 5
4 3
1 3
The domain is {1,3,4}, right?

Answer 52

@ro561man still there?

Answer 53

yeah Im reeading your question/ statement

Answer 54

Yes because x is the domain right?

Answer 55

right.
The question we want to answer is: "are we able to find a single value of y for every value of x."

Answer 56

what do you mean when you say single value of y

Answer 57

So we begin mentally find the ordered pairs
(1, )
(3, )
(4, )
Are you able to complete the ordered pairs without contradiction?