Question

I understand that this

double grade(int &hw) {}

is passing an argument by reference. And that this

double a;
double &b = a;

is making b a reference to a.

But what about this

istream &read_hw(istream &in) {}

What does the reference operator before the name of the function signify, and in what cases would the effect be desired?

Answer 1

This is the type of the return value. In that case, a istream & is returned, so a reference to an istream object.

This is desired if the returned value is meant to be modified by the caller. E.g. you can return a reference to an member variable to make it modifyable

class X {
private:
  int i_;
public:
  int &i() {return i_;}
  const int &i() const {return i_;}
};

In such a case, the member i() can be used as getter and setter:

X x;
int a = x.i();
x.i() = 10;

In the your case of iostreams, the method returns a reference to the passed-in istream object, to enable chaining, e.g. like cout << a << b << c, which calls 3 times
ostream &operator << (ostream &, <whatever>)