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

1 Answer
Jim G.
Aug 6, 2016

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]}

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