what are the asymptotes of the function x/x-4? please help?

We cannot have a 0 denominator so we cannot have x = 4 i.e. x = 4 is an asymptote; x/(x - 4) we can write as [(x - 4) + 4]/(x - 4) and if we divide top & bottom by x - 4 we get 1 + 4/(x - 4) so as x ---> + or - Inf, y ---> 1 i.e. the line y = 1 ia a horizontal asymptote; As x ---> + Inf, y ---> 4 + c (c is a very small number) i.e. the graph approaches y = 1 from above; as x ---> - Inf, the graph approaches y = 1 from below. For the vertical asymptote, as x ---> 4 from the left the denominator is +ve so y ---> + inf; as x ---> 4 from the right, the denominator is -ve so y ---> - Inf. Hope that helps.