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Variation Functions
- 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.
- y=kx/z
- Combined Variation
- y=k/x^n
- 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.
- 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.
- Converse of 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.
- The Fundamental Theorem of Variation
- y=kxz
- Joint Variation
- y=kx^n
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