# Variation Functions 2

### Description

All the variation relations
Mind Map by mar-tamayo, updated more than 1 year ago
 Created by mar-tamayo over 6 years ago
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## Resource summary

Variation Functions
1. Direct
1. n=1
1. Domain and Range are the set of all real numbers
2. n=2
1. Domain: set of all reals Range: [y:y>0]
1. Domain: set of all reals Range: [y:y<0]
1. Combined
1. 3 or more variables that are in a function
1. y-Kx^2/z
2. Joint
1. 3 or more variables that are being multiplied
1. y-kxz
3. Inverse
1. n=1
1. Domain and Range:[x:x= 0]
1. Asymptotes: x-axis and y-axis
1. n=2
1. Domain: [x:x=0] Range: [y:y >0]
1. Domain: [x:x=0] Range: [y:y <0]
1. Asymptotes y-axis and x-axis
2. Fundamental Theorem of Variation
1. If y=kx^n, that is If y varies directly as x^n, then when x is multiplied. If y=k/x^n, that is y varies inversely as x^n, and x is multiplied by a non-zero constant c, then y is divided by c^n by c, y is multiplied by c^n
2. Converse of Fundamental Theorem
1. 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=k/x^n. If multipying 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

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