Answer
a) no; b) $-1; (-2,-1)$; c) $-8; (-8,2)$
Work Step by Step
We are given the function:
$f(x)=\dfrac{x}{x+4}$
a) Check if the point $\left(1,\dfrac{1}{4}\right)$ is on the graph of $f$:
$\dfrac{1}{1+4}\stackrel{?}{=}\dfrac{1}{4}$
$\dfrac{1}{5}\not=\dfrac{1}{4}$
Therefore the point $\left(1,\dfrac{1}{4}\right)$ is not on the graph.
b) Compute $f(-2)$:
$f(-2)=\dfrac{-2}{-2+4}=-1$
The point on the graph is $(-2,-1)$.
c) Solve the equation $f(x)=2$:
$\dfrac{x}{x+4}=2$
$x=2(x+4)$
$x=2x+8$
$x=-8$
The point on the graph is $(-8,2)$.