Functions

Check in the histogram-fitting page how to fit histograms with functions

How to define a function with predefined components
TFormula contains the list of predefined functions.

TF1 *f1 = new TF1("f1", "sin(x)", -5., 5.); // built-in
TF1 *f1 = new TF1("f1", "x*sin(x)", -2., 2.); //combined
TF1 *f1 = new TF1("f1", "[0]*x + [1] + gaus(2)", 0., 15.); // gaus(2) means that parameter numbering starts at 2
f1->SetParameters(0.1, 10., 50., 0.5, 0.01); // need to set initial parameters for non-trivial functions before fitting

TF2 *f2 = new TF2("f2", "sin(x)*sin(y)", -10., 10., -10., 10.);

How to define a user-defined function
In a file myfunc.C define

double myfunc(double *x, double *par) {
double arg = 0;
if (par[2]) arg = (x[0] - par[1])/par[2];
return par[0]*TMath::Exp(-0.5*arg*arg);
}

Load this macro and define a function with it:
.L myfunc.C
TF1 *f1 = new TF1("f1", myfunc, -1., 1., 3); // where 3 is the number of parameters for the function

How to draw a function
There are several specific and general options:
f1->Draw(); // default
f1->Draw("p"); // markers
f1->Draw("h"); // histogram
f2->Draw("surf1"); // For better colors do gStyle->SetPalette(1) and plot again
Note that you may need to set the markers to something sensible before getting output:
f1->SetMarkerStyle(20);
f1->SetMarkerSize(1.0);
f1->SetMarkerColor(kBlue);
It may also be that you need to set the parameters to your function before drawing them, e.g.
TF1 *f1 = new TF1("f1", "gaus");
f1->SetParameters(1000., 0., 1.);
f1->Draw();