Question

Long divide

Answer 1

vertical asymptote

Answer 2

how do I long divide this to find the vertical asymptote of the function and the range ?

Answer 3

Remember that you can divide in parts so that (3x-1)/x is the same as (3x/x) - (1/x).
The 3x/x can be simplified to 3. When you graph this function, it is just 1/x shifted up 3 spaces. For example if x = 1, y = 3 + 1/1 = 4.

As for the asymptote, it is at x = 0 because 1/x is not defined when x = 0.

Answer 4

(long division is for horizontal or slant asymptotes, not vertical asymptotes, but yeah, that's a way to do it.)