Question

Help : Determine if y=2x+1 is a function.

Answer 1

how do you determine it?

Answer 2

yea it is .....

Answer 3

Yes it is very much a function?
What conditions are required for determining?

Answer 4

if every x has a different y then yes it is

Answer 5

angela; that is not quite right, might be lost in translation tho

Answer 6

Btw Thank you all for jumping in to help me I do not see this happen to every ones problem :P

Answer 7

if every x value produces a single y value

Answer 8

amistre?
why?
if a a x produces two y values then???

Answer 9

Crap is it ok to give a good answer to every one who helped? :S they are all good :P

Answer 10

hmmmm...tht's wht i meant Amistre :)

Answer 11

the actual function is
\[\{(x,y)|y = 2x+1\}\]

Answer 12

a function is defined as a special relation in which the dependant variable can be mapped onto only one range element. So that when we are trying to determine the results of a given model we can predict an outcome

Answer 13

It is a copy of the problem i can send pic if you like?

Answer 14

if you want a function you really have to write it as one. so we say
\[y=2x+1\] DETERMINES a function, not IS a function

Answer 15

y^2 = x+2; can be graphed, and if we use a conventional system of a vertical y axis and a horizontal x axis; each x value produces 2 results

Answer 16

determines a function is good :)

Answer 17

A function is a subset of a Cartesian (e.g. \(\mathbb{R}\times\mathbb{R}\) )product such that, if (x,a) and (x,b) are in the subset then a=b

Answer 18

so a relation in which one x produces two y's is not a function?
then what is it called?
for eg
x^2=y?

Answer 19

x^2 =y can be considered a function; if we use conventional graphing means

Answer 20

y^2=x i mean

Answer 21

what do you mean by conventional ?

Answer 22

x=y^r is only a funtion if r=1

Answer 23

I think i got lost lol

Answer 24

the standard graphing system denotes y as a vertical axis and x as a horizontal axis

Answer 25

if those conventions are not kept than all bets are off :)

Answer 26

got it : )

Answer 27

that helped :D

Answer 28

but we can plot y^2=x on a graph using conventions too no?

Answer 29

plotting is a result of being a "relation". A function is a "special type of relation"

Answer 30

So are these relations classified further?
and what are the classes then?

Answer 31

and a one to one relation is a special type of "function" lol

Answer 32

one is to many is a function?
but many is to one is not
ight?

Answer 33

wow thank you so much for helping me under stand it :D i love how there are like 15 people looking at my problem :D

Answer 34

the whole gambit of classes or relations, i dont think I know of; just the basic few

Answer 35

It should be noted that a graph is a function. In fact you are just setting up a injective map between the function (set of ordered pairs) and \(\mathbb{R}^2\) the vector space.

Answer 36

one to one is a function that has an inverse

many to one can be a function

one to many is a relation

Answer 37

ok i have a question how is function determined in 3d space

Answer 38

ya exactly! How can we talk of function in 3 dimensions>?

Answer 39

easy; when i swing a hammer in 3d space; the function is to drive a nail :)

Answer 40

right!
but what are the conditions that will apply?
like for 2 dimensions?

Answer 41

but how do you say that it is function

Answer 42

we can also take angular displacement or angular velocity as a function in 3 dimension.

Answer 43

as long as what your mapping and what your mapping onto conforms to the standards; its good

Answer 44

\[f:\mathbb{R}\to\mathbb{R}^3\]\[f:\mathbb{R^3}\to\mathbb{R}\]\[f:\mathbb{R^3}\to\mathbb{R^3}\]
Do you see now talking about functions in 3-space is ambiguous.

Answer 45

In fact you are just setting up a injective map between the function (set of ordered pairs) and R2 the vector space. I couldnt get this alchemista.

Answer 46

What does that mean?
r^2??
r means Real numbers?

Answer 47

When you raise a field to a power you are taking the Cartesian product of the field

Answer 48

\[\mathbb{R}^2 = \mathbb{R}\times \mathbb{R}\]

Answer 49

R^3 means you are taking the cartesian product twice?

Answer 50

\[\mathbb{R}^3 = \mathbb{R} \times \mathbb{R} \times \mathbb{R}\]

Answer 51

that would be an (x, y, z), where x, y, and z are real numbers.

Answer 52

f:R→R3
f:R3→R
f:R3→R3

Do you see now talking about functions in 3-space is ambiguous.
why is it ambigious then?

Answer 53

I said it was ambiguous because when you talk about functions in 3space it could mean more than one thing.

Answer 54

From which space to which space?

Answer 55

This is good stuff right here xD

Answer 56

Can you give an example alchemista?

Answer 57

I just showed you above, those three examples you pasted again.

Answer 58

no no
an example
can you explain by taking a function?

Answer 59

Oh err someone else think of a real world example

Answer 60

What do you want an example of? a function from R^3 to R^3? or R^3 to R? or whatever combination? lol

Answer 61

sphere is it a function in 3d space

Answer 62

A combination which shows that three dimensional function can be ambiguous?

Answer 63

a sphere is a set of points in R^3 that satisfy some condition.

Answer 64

No, I said that when you said a 3d function, it doesn't tell us what you mean. Not that a function is ambiguous.

Answer 65

yes a sphere can be a good example

Answer 66

i think i should read and then talk with you guys

sorry for the trouble

Answer 67

I think what alchemista is saying is that if you just say "a 3d function", its ambiguous because we dont know what the inputs and outputs are.

Answer 68

See final query here
Like a relation in a 2 dimensional convention be not a function can similarly a case in 3 dimensional relation occure?
Yes or no
plz give 1 eg if possible..
yes ishaan i feel the Same now

Answer 69

You have to be more specific, like, "a function from R to R^3" that tells us it takes in one dimensional objects and spits out 3 dimensional objects

Answer 70

Yes joemath that's what I mean

Answer 71

http://en.wikipedia.org/wiki/Three-dimensional_graph

look at his so unusual ..i never saw something like that

Answer 72

ok say a function from r^3 to R^3

Answer 73

Give me one eg of such a function

Answer 74

T(x,y,z) = (x+y, y+z, x+z)

Answer 75

in theory you have to do that anyway. to specify a function you are supposed to define the domain and range no matter what dimension you are in

Answer 76

thats true satellite.

Answer 77

why is it r^3 to r^3 but?
I am not getting that!

Answer 78

which is why math teachers should stop with problems that say "find the domain of..."

Answer 79

Lets just start with linear transformations

Answer 80

Something from R^3->R^3 could take some point in 3space and rotate it for instance.

Answer 81

its R^3 to R^3 because your input is 3 tuple (did i say that right?)

Answer 82

You can't really graph that.

Answer 83

yeah =/

Answer 84

sorry i didn't knew that

Answer 85

yes alchemista.. i took a point in 3-d n rotated it then??

Answer 86

Oh i think i am taking it in a wrong way..
Sorry for the trouble
i will do some more research and ask
thanks for your time too

Answer 87

<.< ask some more lol

Answer 88

wow you all or just grate

Answer 89

is sin(x+y+z) a function?

Answer 90

hmm... if you say "its a function from R^3 to R" then yes :P

Answer 91

because you need 3 inputs for it to great one output.

Answer 92

its a f(x,y,z) = k or whatever 4th variable you want to use lol

Answer 93

to create* i dont know why i said great lol

Answer 94

Oh yes!
now i get it!
3 inputs to 1 output
makes it a R^3-R function right?

Answer 95

right.

Answer 96

well yes yes i got it!!

Answer 97

an example of a function from R^3 to R we use all the time is volume.
V(l,w,h) = l*w*h
three inputs, a one dimensional output.