Question

Give an example of a rational function that has a horizontal asymptote of y = 2/9?

Answer 1

If you want a horizontal asymptote of y = c (where c is any constant) a worthy candidate is
\[\Large f(x) = \frac1{x - c}\]

Answer 2

no i don't think so

Answer 3

can i use the example of y=(2x+5) / 9x

Answer 4

if you wanted a "vertical" asymptote that would do, but for a horizontal asymptote you want
yes

Answer 5

Crud... sorry guys, fail :3

Answer 6

\[y=\frac{2x+5}{9x}\] will do

Answer 7

how would i go to find the asymptote of this

Answer 8

More like
\[\Large f(x) = \frac1{x}+c\]

Answer 9

do i set both the denominator and numerator to zero?

Answer 10

numerator and denominator have the same degree and the ratio of the leading coefficients is \(\frac{2}{9}\)

Answer 11

But the asymptote was given in the question?

Answer 12

yes but i need to find an equation that fits the asymptote

Answer 13

for example, the horizontal asymptotes of
\[y=\frac{2x^2+6x-8}{9x^2+7x-2}\] is also \(\frac{2}{9}\)

Answer 14

you found one already

Answer 15

how do i find the horizontal asymptote?

Answer 16

It's \(\large y = \frac29\) as it has been written?

Answer 17

i know but step by step

Answer 18

Ahh, I see, well, if you the equation you gave...
\[y=\frac{2x+5}{9x}\]
Then just take the limit as x gets bigger without bound...
\[\large \lim_{x\rightarrow\infty}\frac{2x+5}{9x}\]
And you'll find the (horizontal) asymptote...

Answer 19

y = (2x + 5)/(9x)
lim y = 2/9
x-> ∞
and
lim y = 2/9
x-> -∞
but y never equals 2/9

Answer 20

like this?

Answer 21

Yes, like that.

Answer 22

ok thank you very much :)

Answer 23

Sorry about that first one... gotta think these things through :3
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Terence out