Question

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

Answer 1

use below :
\(\large \frac{\color{red}{a}x+b}{\color{red}{c}x+d}\)

has a horizontal asymptote af \(y = \frac{\color{red}{a}}{\color{red}{c}}\)

Answer 2

give the leading coefficient of the numerator a 2, and the leading coefficient of the denominator a 9 and write whatever you want top and bottom so long as the degrees are the same

Answer 3

you could write what @ganeshie8 wrote, or you could write
\[y=\frac{2x^2+3x-4}{9x^2-5x}\] or anything you like

Answer 4

2x+b / 9x+d
whats b and d?

Answer 5

makes no difference
all you care is that the degrees are the same and the ratio of the leading coefficients is \(\frac{2}{9}\)

Answer 6

just put some numbers for b and d

Answer 7

okay and x?

Answer 8

or be a wise guy and write
\[\frac{2x^{37}+1}{9x^{37}-5}\]

Answer 9

.-.what?

Answer 10

Lol, good job satellite.

Answer 11

make the degree of the top the same as the degree of the bottom and the ratio of the leading coefficients \(\frac{2}{9}\)
@ganeshie8 had the degree of the top and bottom both 1, i.e. \(\frac{2x+something}{9x+whatever}\) but it makes no difference so long as the degrees are the same

Answer 12

2x+1 / 9x+1?

Answer 13

that will certainly work

Answer 14

yay thanks ^.^

Answer 15

yw