Question

y=(2x+3)/(x-4) ; find vertical and horizontal asymptote

Answer 1

As x approaches inf y approaches 2
As x approaches 4, y approaches inf

So vert is 4 and horizontal is 2

Answer 2

Can you show me the method? After got the answer, I need to sketch the function.

Answer 3

for the vertical asymptote...jus find the number which will make the function undefined ie the value of x which will make the denominator have a value of zero...in this case....x-4=0..hence x=4

Answer 4

for the horizontal asymptote..there are many approaches to that one ..i prefer simplifying that expression to y(x-4)=2x+3......yx-4y-2x-3=0...x(y-2)-4y-3=0...then equate the quoficient of the highest power of x to zero..in this case y-2=0'''hence y=2