How to "draw" the function/wave to send symbols using QAM?
The baseband QAM signal is complex, and the only way to draw it is by doing two drawings, one for the in-phase (real) component, and one for the quadrature (imaginary) component.

The passband QAM signal, though, is real, and it is a pulse-shaped carrier whose amplitude and phase depend on each symbol. Myself, I would "draw" it using Matlab or some other numerical program. I don't see the point in trying to draw it by hand.

For example, in Matlab, assuming QPSK and transmitting three symbols with a rectangular pulse shape, at a rate of one symbol per second and a carrier of 5 Hz:

t = 0:0.01:2.99;
p = ones(1,100);         % pulse shape
s = [1+1i, -1-1i, 1-1i]; % symbols to transmit
u(1:100:201) = s;
qam_bb = conv(u,p);      % pulse shaping to generate baseband signal
subplot(3,1,1);
plot(t,real(qam_bb)); title('Baseband In-Phase'); axis([0 3 -1.3 1.3]);
subplot(3,1,2);
plot(t,imag(qam_bb)); title('Baseband Quadrature'); axis([0 3 -1.3 1.3]);
qpsk = real(qam_bb.*exp(2*pi*5*t*1i));  % upconvert baseband signal
subplot(3,1,3);
plot(t,qpsk); title ('Passband QPSK');


produces this plot: