Question about my image dealing with domain

Oct 2017
39
0
Rumba
Z -> R where f(x) = x^2

Domain is Z
Codomain is R

Image i'm not entirely sure about,

I got {0,1,4,9...}

Am i correct to say this?
 
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romsek

Math Team
Sep 2015
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1,552
USA
domain is $\mathbb{Z}$

codomain is $\mathbb{R}$

range is $\{0\}\cup \{n^2: ~ n\in \mathbb{N}\}$
 

romsek

Math Team
Sep 2015
2,777
1,552
USA
the range is the image of the entire domain
 
Oct 2017
39
0
Rumba
the range is the image of the entire domain
If z is domain, that includes ...-3,-2,-1,0,1,2,3....

How can the image be the entire domain?

Dont understand what you mean.
 

romsek

Math Team
Sep 2015
2,777
1,552
USA
Image OF the entire domain.

put the whole domain through the function, everything that comes out is the range. This may or may not be the co-domain. In this case it's just a subset of the co-domain.