Variation Functiona

Variation Functions

Inverse Variation
1. y=k/x^n
  1. 1. Combined Variation
      1. y=kx/z
      2. When both direct and inverse variations occur together in a situation, we say the situation is one of combined variation.
Direct Variation
1. y=kx^n
  1. 1. Joint Variation
      1. y=kxz
      2. 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.

Zusammenfassung der Ressource

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