Question.  How do I define a function that takes a vector argument?

Answer.  There are two basic methods.   It´s usually a matter of taste or style as to which method to use.

Method 1: Use a single named pattern variable on the left of the :=  to stand for an arbitrary vector.  And then on the right of the := perform algebraic operations directly upon tthe named variable or else access the individual coordinates by indexing (using [[ ]] ).  For example:

translate[v_] := v + {2, 3}
reflect[v_] := {v[[1]], - v[[2]]}

Method 2: Use a list of two pattern variables on the left of the := to stand for an arbitrary (2-dimensional) vector.  And then on the right of the := operate upon the list or the individual entries of the list.  For example:

translate[{x_, y_}] := {x, y} + {2, 3}
reflect[{x_, y_}] := {x, -y}

Note that the argument as shown in Method 2 is a list (with two entries).  You could, instead, define the function to take two separate arguments:

translate[x_, y_] := {x, y} + {2, 3}
reflect[x_, y_] := {x, -y}

Or, having made the definition that uses the list with two entries, you could simply add the definition:

translate[x_, y_] := translate[{x, y}]
reflect[x_, y_] := reflect[{x, y}]

Conversely, if you have already made the definitions that use one-argument list with two entries..

translate[x_, y_] := {x, y} + {2, 3}
reflect[x_, y_] := {x, -y}

.. then you could make the definition for two separate arguments by invoking the Sequence function, like this:

translate[x_, y_] := translate[Sequence[{x, y}]]
reflect[x_, y_] := reflect[Sequence[{x, y}]]