Let $S=\{0,2,4,6,8\}$, $T=\{1,3,5,7\}$. Determine whether each of the following sets of ordered pairs is a function with domain $S$ and co-domain $T$. 
Let $S=\{0,2,4,6,8\}$ and $T=\{1,3,5,7\}$. Determine whether each of the following sets of ordered pairs is a function with
  domain $S$ and co-domain $T$.



*

*$\{(6,3),(2,1),(0,3),(8,7),(4,5)\}$
TRUE
This is a function

*$\{(2,1),(4,5),(6,3)\}$
FALSE
Not all domain values used

*$\{(0,2),(2,4),(4,6),(6,0),(8,2)\}$
FALSE
Domain values mapped to values outside of co-domain

*$\{(2,3),(4,7),(0,1),(6,5),(8,7)\}$
TRUE
This is a function

*$\{(6,1),(0,3),(4,1),(0,7),(2,5),(8,5)\}$
FALSE
$0$ is mapped twice


Currently, I am unsure about number 3, can the domain values be mapped to itself as shown or does that invalidate it as a function in this situation since the co-domain has specified values? Thanks!

The domain values of a function must be mapped to values in the codomain, so, as indicated in the comments, your work is correct.
