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|dw:1352343487773:dw|
vertical asymptote
how do I long divide this to find the vertical asymptote of the function and the range ?

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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.
(long division is for horizontal or slant asymptotes, not vertical asymptotes, but yeah, that's a way to do it.)
|dw:1352347692738:dw|
how did you get 1/3 ? :S
Vertical asymptotes are where the denominator is equal to zero.
If you meant as your function, \[\large \frac{3x-1}{x}\] Then the vertical asymptote is at x=0. You only use long division to find slant asymptotes.

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