Variation Functiona

Variation Functions

1. Inverse Variation

   • y=k/x^n
     • • Combined Variation
         • y=kx/z
         • When both direct and inverse variations occur together in a situation, we say the situation is one of combined variation.

2. Direct Variation

   • y=kx^n
     • • Joint Variation
         • y=kxz
         • 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.