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# Domain & Range Watch

1. You have y = 1 + x + x^3 no other information have bee given. It is asked what is largest possible domain and corresponding range for this function?
Usually your given domain values or know what the graph looks like but here i am clueless

2. (Original post by Jowhar)
You have y = 1 + x + x^3 no other information have bee given. It is asked what is largest possible domain and corresponding range for this function?
Usually your given domain values or know what the graph looks like but here i am clueless

We have to answer two questions:

1) Are there any values of x which the function won't work for? If not, the domain is going to be . If so, the domain is going to be with the problem points taken away. (For example, if we have then a problem point is x=0.)

2) Are there any values of y that aren't given by our domain? In other words, if I give you any value of y, can you find an x value that gives the y value? If you can, then the range will also be .

I think that x will work for any value including 0 so the domain will R?
If domain values are all R then range values will all be R?

Thank you for you explanation but i dont so much understand 2nd point about range?
4. Can someone give me the answer please? or correct what im thinking?
5. I kind of agree with you.
If the domain is R, then I think the range (aka codomain) should also be R. You have to work out how to justiy it though, a picture is a good start.

I'm bothered by this though:

(Original post by Jowhar)
What is largest possible domain and corresponding range.
"Largest"?
What kind of set theory are you using here? Have you covered complex numbers or quaternions or anything? This is a little vague...
6. (Original post by Jowhar)

I think that x will work for any value including 0 so the domain will R?
If domain values are all R then range values will all be R?

Thank you for you explanation but i dont so much understand 2nd point about range?
Yeah, that's right.

To see how the range might not be the whole of R, imagine . The largest possible domain is , but the range isn't as can't be negative! The range will instead be with .

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Updated: December 18, 2010
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