Question

Find the asymptotes of the following curves:

f(x) = `(x^2 + 6x - 4)/(3x - 6)`

Answer 1

The function becomes undefined when x = 2.

∴ x = 2 is the vertical asymptote.

No Horizontal asymptote exist for the given curve.

Oblique asymptote can be obtained by polynomial long division method.

∴ y = `x/3 + 8/3` or 3y = x + 8 is the slant asymptote.

            `x/3 + 8/3`
`3x - 6")"overline(x^2 + 6x - 4)`
             `x^2 - 2x`
             (–)    (+)           
                     `8x - 4`
                     `8x - 16`
                     (–)     (+)  
                               12