Question

I DONT EVEN KNOW WHERE TO START :(
Give an example of a rational function that has a horizontal asymptote at y = 0 and a vertical asymptote at, x = 2 and x = 1.

Answer 1

hint, the vertical asymptotes will occur where the denominator is zero

Answer 2

so make a quadratic with zeros at \(1\) and \(2\)
is it clear how to do that ?

Answer 3

well what do you mean by quadratic for the zeros

Answer 4

what polynomial has zeros at \(x=1\) and \(x=2\) ?
hint, write it in factored form

Answer 5

factored for as in x-1=0 and x-2=0??

Answer 6

right but actually i meant as \((x-1)(x-2)\) that is your denominator

Answer 7

so (x-1)(x-2) is all my denominator, but i dont get how i would come up with the numerator

Answer 8

would it just be one?

Answer 9

what is the degree of your denominator?

Answer 10

yeah you could use \(1\) that would work
\[\frac{1}{(x-1)(x-2)}\] would work

Answer 11

so would any number up top

Answer 12

and since your denominator is of degree 2, a degree1 polynomial up top would work as well
for example
\[\frac{x}{(x-1)(x-2)}\]

Answer 13

ohh because of the rule where if the numerator degree is < the denom degree the asymptote is 0

Answer 14

so this would count as a rational equation for the question. im not missing anything right? 1/(x-1)(x-2)