Question

I need to know how to write a rational function by only knowing the vertical and horizontal asymptotes.

Answer 1

do you have x and y?

Answer 2

yes. All i have is Vertical asymptote at x = 5 and a horizontal asymptote at y = 1/2

Answer 3

If there is a vertical asymptote at x = 5, then x-5 is a factor of the denominator.
If there is a horizontal asymptote at y = 1/2, that tells you that the degrees of the numerator and denominator are the same and the ratio of the coefficients of the leading terms is 1/2

Answer 4

ok now what?

Answer 5

You're done

Answer 6

but all i know is the denominator

Answer 7

even read his comment ;)

Answer 8

ya im confused

Answer 9

why?

Answer 10

i dont understand

Answer 11

you should practice more read carefully what he write and practice the best thing is like if really you dont understand come again :)

Answer 12

? i under stand what he is saying about the vertical asymptote but i don't understand the horizontal asymptote.

Answer 13

Do you know what is meant by the degree of the numerator and denominator?

Answer 14

yes x or x^2 or x^3 etc

Answer 15

So, if I have a numerator of x^3-5x^2+6x-9, what is the degree of the numerator?

Answer 16

x^3

Answer 17

The degree is 3.

Answer 18

ya

Answer 19

So earlier I told you that if the degrees of the numerator and denominator are the same, then the horizontal asymptote is the ratio of the coefficients. Do you know what coefficients are?

Answer 20

the number before the variables?

Answer 21

And it is the ratio of the coefficients of the leading terms and the leading terms are the ones that determine the degree.

Answer 22

So...an example

Answer 23

\[f(x)=\frac{3x+2}{x-2}\]

Answer 24

Do you see that the degrees of the numerator and denominator are equal?

Answer 25

yes

Answer 26

Do you see that the leading term of the numerator is 3x and of the denominator is x?

Answer 27

yes so it would be 3/1?

Answer 28

So the horizontal asymptote is y = 3. Yes. and there is a vertical asymptote at x=2

Answer 29

Can you do your problem now?

Answer 30

so would \[\frac{ x + 10 }{ 2x - 10 }\] work??

Answer 31

That will work. Good for you.

Answer 32

Thanks!

Answer 33

yw