Question

Find an equation for a rational function with the following properties:

vertical asymptotes at x=1 and x=−9
zero at x=11
f(0)=15
horizontal asymptote at y=0

please check my work thanks
I got:
15(x-11)^2/(x-1).(x+9)

Answer 1

too bad you didn't go to an online graphing site to check it out
15(x-11)^2/(x-1).(x+9)
has a horizontal asymptote of y=15 since top and bottom have the same degree.
If you want the asymptote at y=0, you need the top to have a lower degree than the bottom. So, I'd start with
y = (x-11)/(x-1).(x+9)
Now, that has f(0) = -11/(-1*9) = 11/9
So you need 15 * 9/11 (x-11)/(x-1).(x+9) = 135(x-11) / 11(x-1)(x+9)
the graph is at

www.wolframalpha.com/input/?i=135%28x-11%29+%2F+%2811%28x-1%29%28x%2B9%29%29+for+-10%3C%3Dx%3C%3D10

Answer 2

Thank you, oobleck