Posted by Gretchen on .
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)

Calc 
Steve,
Looks like the function has (x5) in the denominator, but not the numerator.
??/?(x5)
It has (x1) both top and bottom, because it's otherwise continuous there.
?(x1)/(x1)(x5)
x=2 when y=0
(x2)(x1)/(x1)(x5)
limit is 1/9 at x=1
4(x2)(x1)/9(x1)(x5)
f(0) = 8/45
as x gets large, f(x) approaches 4/9