How do I find the asymptotes of #y=7/(3x-4)-1/9#?

1 Answer
Aug 6, 2016

Answer:

vertical asymptote #x=4/3#
horizontal asymptote #y=-1/9#

Explanation:

The denominator of y cannot be zero as this is undefined. Equating the denominator to zero and solving gives the value that x cannot be and if the numerator is non-zero for this value then it is a vertical asymptote.

solve: 3x - 4 = 0 #rArrx=4/3" is the asymptote"#

Horizontal asymptotes occur as

#lim_(xto+-oo),ytoc" (a constant)"#

divide terms on numerator/denominator by x

#(7/x)/((3x)/x-4/x)-1/9=(7/x)/(3-4/x)-1/9#

as #xto+-oo,yto0/(3-0)-1/9#

#rArry=-1/9" is the asymptote"#
graph{(7)/(3x-4)-1/9 [-10, 10, -5, 5]}