Answer
(a) $\{x|x\ne1\}$,
(b) not on the graph,
(c) $ 4$, $(3,4)$,
(d) $x=\frac{7}{4}$ , $(\frac{7}{4},9)$
(e) rational function.
Work Step by Step
Given $f(x)=\frac{x+5}{x-1}$, we have:
(a) The domain $\{x|x\ne1\}$,
(b) $f(2)=\frac{2+5}{2-1}=7\ne6$, thus $(2,6)$ is not on the graph,
(c) $f(3)=\frac{3+5}{3-1}=4$, thus $(3,4)$ is a point on the graph,
(d) $\frac{x+5}{x-1}=9\Longrightarrow x+5=9x-9 \Longrightarrow x=\frac{7}{4}$ and $(\frac{7}{4},9)$ is a point on the graph,
(e) $f(x)$ is a rational function.
