1) Generally, it'll be a closed circle. It behaves similar to say, y = x/x, which is equal to 1 as long as x =/= 0. So in a similar fashion, the reciprocal of 1/x is 1/(1/x), which is equal to x as long as x =/= 0.

Here's a relatable post: https://math.stackexchange.com/quest...at-is-cot-pi-2

2) Doesn't really matter, as the examiner will only care about the general behaviour of the curve (i.e. whether it's increasing or decreasing). Personally, I'd plot them as curves since we shouldn't assume the original graph to be a hyperbola.

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