I have only been able to find one way for functions to take a variable amount of arguments. It's this way:

#include <iostream>
#include <stdarg.h>

using namespace std;

void Print(int argumentAmount, ... );

int main()
{
    Print(5,11,22,33,44,55);
}

void Print(int argumentAmount, ... ){

    va_list arguments; 
    va_start(arguments, argumentAmount);

    int parameter;
    for(int i = 0; i < argumentAmount; ++i ){
        parameter = va_arg(arguments, int);
        cout << parameter << endl;
    }

    va_end(arguments);
    return;
}

2 Problems: 1.) I have to specify how many arguments I'm sending in- not desirable 2.) I can't figure out how to modify it so it will output strings.

Would something like this be possible without having to overload the function multiple times:

void Output(/*not sure how this would look*/);

int main(){

    Output("hello","world");
    Output("this","is","a","test");
    Output("As","many","strings","as","you","want","may","be","passed","in");

    return 0;
}
void Output(/*not sure how this would look*/){

    //loop through each string passed in and output it
}

What about this:

void Capitalize(/*all passed by reference*/);

int main(){

    string s1 = "hello";
    string s2 = "world";

    string s3 = "this";
    string s4 = "is";
    string s5 = "a";
    string s6 = "test";

    string s7 = "as";
    string s8 = "many";
    string s9 = "strings";
    string s10 = "as";
    string s11 = "you";
    string s12 = "want";

    Capitalize(s1,s2);
    Capitalize(s3,s4,s5,s6);
    Capitalize(s7,s8,s9,s10,s11,s12);

    return 0;
}
void Capitalize(/*all passed by reference*/){

    //capitalize each string passed in

}

All I can think to do is: -overload the function multiple times -have the function accept some type of container instead

If this is NOT POSSIBLE, could someone explain why the compiler is not capable of accomplishing a task like this.

With variadic templates in C++11, you can do something like this (see the result at ideone)

#include <string>
#include <iostream>

void Output() {
    std::cout<<std::endl;
}

template<typename First, typename ... Strings>
void Output(First arg, const Strings&... rest) {
    std::cout<<arg<<" ";
    Output(rest...);
}

int main() {
    Output("I","am","a","sentence");
    Output("Let's","try",1,"or",2,"digits");
    return 0;
}