Question

A rational function f(x) contains quadratic functions in both the numerator and denominator. Also the function f(x) has a vertical asymptote at x=5, a single x intercept of (2,0) and f is removeably discontinuous at x=1 because the lim x-> 1 is -1/9.

Find f(0) and lim x-> infinity of F(x)

Answer 1

Looks like the function has (x-5) in the denominator, but not the numerator.

??/?(x-5)

It has (x-1) both top and bottom, because it's otherwise continuous there.

?(x-1)/(x-1)(x-5)

x=2 when y=0

(x-2)(x-1)/(x-1)(x-5)

limit is -1/9 at x=1

-4(x-2)(x-1)/9(x-1)(x-5)

f(0) = -8/45
as x gets large, f(x) approaches -4/9