asymptote F(x)=7+9/(x-3)

Question

horizontal asymptote of F(x)=7+9/(x-3)?

Answer 1

for horizontal asymptote, it needs to find the y-value where it cannot be define

 

 

y=7+9/(x-3) original function

 

find the inverse function of this (i.e. basically solve for x-value)

 

y-7 = 9/(x-3)

 

(y-7)(x-3) = 9

 

x-3 = 9/(y-7)

 

x = 3 + 9/(y-7) - this is the inverse function

 

y cannot be 7 since it will be undefined

 

the horizontal asymptote is y=7

 

 

Answer 2

As x→∞, x-3→∞ and as x→-∞, x-3→-∞  

 

So, 9/(x-3)→0 as x→±∞

 

Therefore, as x→±∞, F(x)→7 + 0 = 7

 

Thus, the horizontal asymptote is y = 7.