Answer
a) $k=4$;
b) $k=-1/8$;
c) $k$ can be any real number;
d) $k=1$.
Work Step by Step
In all of the parts we substitute for $y$ the second coordinate of the point and for $x$ the first coordinate of the point into the equation $y=kx^3$ and then we calculate k.
a) $$4=k\times1^3\Rightarrow 4=k$$
So here for $k=4$ the graph passes through point $(1,4)$.
b) $$1=k\times(-2)^3 \Rightarrow 1=k\times (-8)\Rightarrow k = -\frac{1}{8}$$
so for $k=-1/8$ the graph passes through $(-2,1)$.
c) $$0=k\times 0^3\Rightarrow 0=k\times 0.$$
The last equation is true for any $k$ so for every real value of $k$ the graph will certainly pass through $(0,0)$.
d) $$-1=k\times(-1)^3\Rightarrow -1=-k\Rightarrow k=1$$
so for $k=1$ the graph will pass through $(-1,-1)$.
