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

1 Answer
Dec 10, 2016

Answer:

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

Explanation:

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]}