AQA A-Level Further Maths D12-01 Rational Functions: How to Sketch y=(ax+b)/(cx+d)

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I learnt how to find the y value by just dividing the coefficients of x, top coefficient/ bottom coefficient. I know that is what you did as well, but is there a reason we should think about it as you explained it? That we should put the other numbers over x and then they get small to the point where we can ignore them? Or were you just explaining how this all works? Like, is it ok to just think of it as divide the coefficients of x? Also, I don’t know if you have done this in a later video, but how would we go about finding the vertical asymptotes of a function such as, 6x+2/(x-3)(x+2). If you expand it out, you get two values of x when factorise it as a quadratic, I considered if this means that the graph has a parabola, but I am not sure, because it is written in a way that makes me think it is a rational function. Or does this have two vertical asymptotes and that’s why there are two values of x?

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The problem with these new synoptic type of A Level exam is that they want wider knowledge. Although this is officially in further maths... theyl ask you a question like what is the domain or range of a this composite or function/ inverse function and the only way around it is by knowing how to sketch them...

AceOfHearts