Variation Functiona

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nina.0418
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Variation Functions
  1. Inverse Variation
    1. y=k/x^n
        1. Combined Variation
          1. y=kx/z
            1. When both direct and inverse variations occur together in a situation, we say the situation is one of combined variation.
      1. Direct Variation
        1. y=kx^n
            1. Joint Variation
              1. y=kxz
                1. When one quantity varies directly as powers of two or more independent variables, but not inversely as any variable.
                  1. The Fundamental Theorem of Variation
                    1. 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.
                      1. Converse of the Fundamental Theorem of Variation
                        1. 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.
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