When both direct and inverse variations occur together in a
situation, we say the situation is one of combined variation.
When one quantity varies directly as powers of two or more
independent variables, but not inversely as any variable.
The Fundamental Theorem of Variation
1. If y = kxn, that is, y varies directly as xn, and x is multiplied by c, then y is
multiplied by cn. 2. If y =k/x^n, that is, y varies inversely as x^n, and x is multiplied x^n
by a non-zero constant c, then y is divided by c^n.
Converse of the Fundamental Theorem of Variation
a. 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. b. 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.