Answer:
Assuming that the domain is [tex]\lbrace0,\, 1,\, 2,\, 3\rbrace[/tex] (the set of whole numbers between 0 and 3, inclusive,) then only the third choice would represent a function:
[tex]\lbrace{(2,\, 15),\, (3,\, -3),\, (1,\, 3),\, (0,\, 0)\rbrace}[/tex].
Step-by-step explanation:
A function needs to be
A map is one-to-one only if it maps each input to only one output.
For example, in [tex](0,\, 5)[/tex] in the first choice, [tex]0[/tex] is the input while [tex]5[/tex] is the output. If this set of coordinates is indeed one-to-one, then this input,
Similarly, the second set of coordinates tries to map the input [tex]1[/tex] to both [tex]10[/tex] and [tex]2[/tex]. This option isn't one-to-one and does not represent a function, either.
Indeed, the third, fourth, and fifth options are all one-to-one. However, there are gaps in the domain of the fourth and fifth option. (The domain of a map is the set of all the points in its definition.)
Note, that whether these options are functions depend on the choice of the domain. For example, if the domain is merely [tex]\lbrace1\rbrace[/tex], then all three options would be functions. However, if the domain is the set of all integers ([tex]\mathbb{Z}= \lbrace\dots,\, -2,\, -1,\, 0,\, 1,\, 2,\, \dots\rbrace[/tex],) then none of these choices will be a function.
