More help on identifying functions. Please help!

[lillybeth]

OK. Here is my problem:

x	y
-3	1
-4	4
-5	1

Is this a function?



How do I find the answer? (I already know what a function is)

 

[srmichael]

OK. Here is my problem:

x	y
-3	1
-4	4
-5	1

Is this a function?



How do I find the answer? (I already know what a function is)

Lillybeth, this isn't any different than the previous thread you posted about functions. Use what I said in the other thread and get back to us on if you think this is a funtion or not.

 

[lillybeth]

Lillybeth, this isn't any different than the previous thread you posted about functions. Use what I said in the other thread and get back to us on if you think this is a funtion or not.

yes it is a function, i know because someone just told me but I still don' t see how to find out. Can you show me how in the next post? (step by step instructions)

 

[srmichael]

yes it is a function, i know because someone just told me but I still don' t see how to find out. Can you show me how in the next post? (step by step instructions)

Have you heard of the vertical line test to determine if it is indeed a function? If a vertical line crosses a graph in more than one point that is the same as saying that for one x value you have more than one y value. If you can't see this relationship in your coordinates, you may want to plot these points, connect them and then see if a vertical line drawn through your make-shift graph intersects in more than one point. Once you do this a few times you won't have to plot any points to make this determination once you understand this.

Here's an example:

Function: (1,2) (2,2) (3,2)
Not a Function: (1,2) (1,3) (3,2)

So you see in the coordinates representing a function you can have the same y value for different x values, you just can't have the different y values for the same x value (coordinates in red make this not a function).

Does that help?

 

[lillybeth]

Thanks!

(Originaly posted by srmichael) Does that help?

Yes it does. Thanks a lot!!!

 

[JeffM]

yes it is a function, i know because someone just told me but I still don' t see how to find out. Can you show me how in the next post? (step by step instructions)

Lillybeth

I think you may be getting a little confused because these problems involve finite domains. (Have you discussed the domain of a function. The domain of a function is the set of input values for which the function is defined.) In one problem, the function was defined using coordinate notation such as

\(\displaystyle (1, 2),\ (2, 4),\ (3, 6).\)

In a different problem, the function was defined using a tabular form

\(\displaystyle x\ \ y\)

\(\displaystyle 1\ \ 2\)

\(\displaystyle 2\ \ 4\)

\(\displaystyle 3\ \ 6\)

As srmichael has said, a function must produce as output exactly ONE value for every input value in the function's domain. Determining whether something is a function when the purported domain is infinite may call for a bit of conceptual work because you cannot individually test every item in the domain.

But when the domain of the purported function is finite, as it is in these problems, the determination is super easy. I suspect that you are thinking of these problems as implying infinite domains and wondering how you determine anything about them from a small set of examples. But these problems do not involve infinite domains; nothing is told to you about input values other than what you see. They are finite domains.

For a function to be defined for a finite set of input (frequently labeled as x) values, you must have: (1) an output value (frequently labeled as y) for every input value, and (2) either (a) each possible input value is listed just once, or (b) any repeated input value shows the same output value each time.

Do you see why the procedure above conforms to srmichael's general definition?

 

[lillybeth]

thanks!

Lillybeth

I think you may be getting a little confused because these problems involve finite domains. (Have you discussed the domain of a function. The domain of a function is the set of input values for which the function is defined.) In one problem, the function was defined using coordinate notation such as

\(\displaystyle (1, 2),\ (2, 4),\ (3, 6).\)

In a different problem, the function was defined using a tabular form

\(\displaystyle x\ \ y\)

\(\displaystyle 1\ \ 2\)

\(\displaystyle 2\ \ 4\)

\(\displaystyle 3\ \ 6\)

As srmichael has said, a function must produce as output exactly ONE value for every input value in the function's domain. Determining whether something is a function when the purported domain is infinite may call for a bit of conceptual work because you cannot individually test every item in the domain.

But when the domain of the purported function is finite, as it is in these problems, the determination is super easy. I suspect that you are thinking of these problems as implying infinite domains and wondering how you determine anything about them from a small set of examples. But these problems do not involve infinite domains; nothing is told to you about input values other than what you see. They are finite domains.

For a function to be defined for a finite set of input (frequently labeled as x) values, you must have: (1) an output value (frequently labeled as y) for every input value, and (2) either (a) each possible input value is listed just once, or (b) any repeated input value shows the same output value each time.

Do you see why the procedure above conforms to srmichael's general definition?

Yep! I do. Thanks for the help!