# Variation Functiona

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 Created by nina.0418 about 6 years ago
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Functins

## Resource summary

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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