How do you find the vertical, horizontal or slant asymptotes for $y = (4 x + 6)/(x - 1)$ ?

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Answer 1 · 2016-12-10T10:04:14

We have a vertical asymptote at $x=1$ and horizontal asymptote at $y=4$ .

As $x-1->0$ i.e. $x->1$ , $y->oo$ and hence, we have a vertical asymptote given by $x=1$ .

Further, we have $y=(4x+6)/(x-1)$ and dividing numerator and denominator on right hand side by $x$ , we get

$y=(4+6/x)/(1-1/x)$

and hence, as $x->oo$ , $y->4/1=4$ i.e. we have a horizontal asymptote $y=4$ .

graph{(4x+6)/(x-1)[-20,20,-10,10]}

How do you find the vertical, horizontal or slant asymptotes for y = (4 x + 6)/(x - 1)y = (4 x + 6)/(x - 1)?