If y varies directly as x^n, then
when x is multiplied by c, y is
multiplied by c^n. If y varies
inversely as x^n, then when x
is multiplied by c, y is divided
by c^n.
Converse of
Fundamental Theorem
If multiplying every x-value of a function
by c results in multiplying the
corresponding y-values by c^n, then y
varies directly as the nth power of x, that
is, y = kx^n. If multiplying every x-value of
a function by c results in dividing the
corresponding y-values by c^n, then y
varies inversely as the nth power of x,
that is, y = k/x^n