As sin(theta) in [-1,1], the x prior to sin(1/x) acts as a scaling factor. As x grows large, the amplitude of the oscillations of the sine function also grow. Similarly, as x approaches 0, the amplitude shrinks.
Next, looking at sin(1/x) we note that 1/x->oo as x->0. This means that as x->0 the sine function cycles through periods of 2pi more and more rapidly. Similarly, 1/x->0 as x->+-oo, meaning it will take greater and greater changes in x to go through a full period of 2pi. After |x| > 1/(pi) there will be no further oscillations, as we will have |1/x| in (0,pi).
The resulting graph will have oscillations which grow in amplitude and are stretched further apart as x is further from 0, soon ceasing to oscillate at all, and which have smaller amplitudes and wilder oscillations closer to 0.
graph{xsin(1/x) [-1.5, 1.5, -0.75, 0.75]}
