programming - How can I use Max[] in a function that is passed a list not find the max of the list

For most functions in Mathematica, passing them a list will call the function on each element of the list. For example:

ExampleFunction1[x_] := x + 1
ExampleFunction1[{1, 2, 3}] 
(* {2, 3, 4} *)

But things change when you use Max[]. For example if I have this function:

ExampleFunction2[x_] := Max[x, 4] 

If I pass this a single number x, it will return either x or 4, whichever is larger, but, as documented, if i pass it a list like this:

ExampleFunction2[{1, 3, 7}] 

It will return 7. Instead I'd like it to return { 4, 4, 7}.

How can I make my function so that Max uses an element of a list as its argument instead of the entire list?