## anonymous 3 years ago Long divide

1. anonymous

|dw:1352343487773:dw|

2. anonymous

vertical asymptote

3. anonymous

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

4. anonymous

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.

5. anonymous

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

6. anonymous

|dw:1352347692738:dw|

7. anonymous

how did you get 1/3 ? :S

8. anonymous

Vertical asymptotes are where the denominator is equal to zero.

9. anonymous

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.