(Note this is the kind of exercise I would ask someone who is doing further maths and especially someone MAT/STEP) Sketch the graph of y=sin(1/x)

First of all we want to think about the general behaviour of the function. Does it grow as x grows? Does it oscillate? Does it tend to a limit? We also need to think about if there are any worrying points in the graph. Clearly here we will need to think about the point x=0, but for now let's avoid it as dealing with the rest of the graph may help give us a clue to what the answer to that might be. It is helpful to draw sinx and 1/x first. As for general behaviour, we know sinx is bounded by +1/-1 so the graph will remain in between 1 and -1 for all values of x and it will have some form of oscillatory behaviour. As the modulus of x gets bigger 1/x gets smaller and if we think of how sinx simply gets smaller and smaller once x is less than pi/2, we know that y=sin(1/x) is going to tend to zero as x tends to +/- infinity. From which side of the x axis? Well when x is negative and large, 1/x is small and negative so we have that the graph goes from below to the left of the y axis and from above to the right. As we head towards 0, the graph will oscillate between +1/-1, and seeing as the gradient of y=1/x increases towards zero, the frequency of the oscillations will increase. Now what about zero? Well it will keep oscillating faster and faster as we get closer so in short, we don't know! It is not defined!https://www.desmos.com/calculator/plchxiojak