Question

Find an expression for a rational function f(x) that satisfies the conditions: a horizontal asymptote at y = 0, vertical asymptotes at x = ±3, and contains the point (0, 1).

Answer 1

@xapproachesinfinity

Answer 2

so on the bottom we know we are going to have what factors?

Answer 3

x=3 will make the bottom zero
so x-3 is going to be on bottom
you also know x=-3 will make the bottom zero
so what other factor is on bottom

Answer 4

I got f (x) = -9 / x^2 - 9

Answer 5

\[f(0)=\frac{-9}{0-9}=\frac{-9}{-9}=1 \]
yep looks good

Answer 6

you have the ordered pair (0,1) on f
you also have the horizontal asy y=0
and the vertical asymyptotes x=-3,x=3

Answer 7

Write a general formula to describe the variation: x varies inversely with the cube of y.
I got x = k/y^3 for thid one

Answer 8

for the y=0 part we just needed the degree on bottom to be bigger than the degree on top

Answer 9

oh okay

Answer 10

y varies inversely as the value of x
can be translated as y=k/x

Answer 11

so you are correct

Answer 12

Awesome!

Answer 13

Ok I have one or two more problem