continuous function

[porednata]

1. The problem statement, all variables and given/known data
Do the graphic rendering (and write the full proof) of the function h : [0,1) -> \Re , which is continuous and bounded but does not reach it's bounds.

2. The attempt at a solution
If h is continuous : exists
lim h(x) = h(x0)
x->xo
If h is bounded:
А ≤ h(x) ≤ В for every x\in[0, 1)

I thought that the function f(x) = \frac{sin\frac{1}{1-x}}{2-x}
works but I can't quite do the proof and the graphic rendering which leads me to the point that I'm wrong. Pls help :confused:
f(x) = \frac{sin\frac{1}{1-x}}{2-x} 's graphic rendering :
18823
is this right?!