Answer
(a) The domain is $(-\infty,1)\cap(1,\infty)$
(b) (2,6) is not on the graph.
(c) f(x)=4
(d) x=1.75
(e) f(x) is a rational function.
Work Step by Step
(a) There is a vertical asymptote at x=1; therefore the domain is $(-\infty,1)\cap(1,\infty)$
(b) Let's find f(2) to see if it equals 6:
$f(2)=\dfrac{2+5}{2-1}=\dfrac{7}{1}=7$
It doesn't, so (2,6) is not on the graph.
(c) To find out, let's calculate f(3):
$f(3)=\dfrac{3+5}{3-1}=\dfrac{8}{2}=4$
(d) To find out, let's replace f(x) with 9 and solve for x:
$9=\dfrac{x+5}{x-1}$
$9\cdot (x-1)=\dfrac{x+5}{x-1}\cdot (x-1)$
$9x-9=x+5$
$9x-x-9+9=x+5-x+9$
$8x=14$
$x=\frac{14}{8}=1.75$
(e) Polynomial functions don't have negative degrees, while rational functions do; therefore, f(x) is a rational function.