Question

Alicia is writing the program for a video game. For one part of the game, she uses the rule

Answer 1

As the mapping suggests, the first (x) coordinate is decreased by 3, and the second (y) coordinate is increased by 2. So, given the inputs, you have

$(-2,0) \mapsto (-2-3, 0+2) = (-5,2)$

$(3,-4) \mapsto (3-3, -4+2) = (0,-2)$

And yes, this rule is a function: it has a starting set (the domain), which is all possible couples $(x,y)$, and a landing set (the codomain), which is again composed by the couples $(x,y)$. Since for every point in the domain you have one and only one output, this rule is a function.