\begin{tikzpicture}[scale=\textwidth/10cm,samples=200]

% Handle
\begin{scope}[shift=(10:7/8), rotate=-30, yslant=1/2, xslant=-1/8]
  \shade [top color=gray!80, bottom color=gray!30] 
    (0,0) arc (130:-100:3/8 and 1/2) -- ++(0,1/4) arc (-100:130:1/8 and 1/4) -- cycle;
  \shade [top color=gray!10, bottom color=gray!60] 
    (0,0) arc (130:-100:3/8 and 1/2) -- ++(0,1/32) arc (-100:130:1/4 and 1/3) -- cycle;
\end{scope}

% Cup
\fill [black!75, path fading=fade out] 
    (0,-1) ellipse [x radius=3/4, y radius=1/2];
\shade [left color=gray!60, right color=gray!30] 
  (-1,0) arc (180:360:1 and 5/4);
\shade [bottom color=gray, top color=gray!30, opacity=1/2]
  (-1,0) arc (180:360:1 and 5/4);
\shade [left color=gray!20, right color=gray!40] 
  (0,0) ellipse [x radius=1, y radius=1/2];
\shade [left color=gray!40, right color=gray!20] 
  (0,0) ellipse [x radius=1-1/16, y radius=1/2-1/16];
\shade [bottom color=gray, top color=gray!10, opacity=1/2] 
  (0,0) ellipse [x radius=1-1/16, y radius=1/2-1/16];
\draw  (0,-1.7) node {$X = $ A Coffee Cup};
\draw[-{Latex[length=3mm,width=3mm]}] (1.5, -.5) .. controls (2, -1) and (2.5, .5)  ..(4.2, -.5);
\draw  (3.0,0) node {$f: X \to Y$};
\end{tikzpicture}