Question

State the horizontal asymptote of the rational function 5x+1/9x-2

I've never done or seen this before, does the rule still apply?

Answer 1

what rule are you thinking of?

Answer 2

horizontal asymptotes are concerned with the end behaviour .... or rather, for very large values of |x|.

Answer 3

as |x| gets large .... that +1 and -2 become insignificant to the problem:

\[\frac{5(1000000000000000000) + 1}{9(1000000000000000000) -2}\approx \frac{5(1000000000000000000)}{9(1000000000000000000)}\approx \frac59\]

Answer 4

So 5/9 would be the horizontal asymptote?

Answer 5

the larger and larger |x| gets, the more insignificant the error becomes as you approach infinity ....

Answer 6

so yeah .... as |x| approaches infinity, the value of this expression approaches 5/9

Answer 7

Okay thanks you, one last thing what would make a vertical asymptote =4

Answer 8

vertical asymptotes are concerned with behaviour in the middle of the ends :) if we have a dividing factor that cannot be canceled out; it must be removed from the domian since it produces an undefined value at that point

Answer 9

\[\frac{x}{x-4}\] is undefined at x=4

Answer 10

thanksss

Answer 11

yw