# Variation Functions

Mind Map by mar-tamayo, updated more than 1 year ago
 Created by mar-tamayo about 6 years ago
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### Description

mind map of direct, inverse, combined, and joint variation

## Resource summary

Variation Functions
1. Inverse
1. n=1
1. hyperbolas
1. asymptotes: x-axis, y-axis
1. n=2
1. inverse square curves
1. asymptotes:y-axis, x-axis
2. Direct
1. n=1
1. lines
1. domain and range: all real numbers
2. n=2
1. parabolas
2. combined variation
1. 3 or more variables in a function
2. joint variation
1. 3 or more variables that are multiplied
3. Fundamental theorem of variation
1. If y varies directly as x^n, then when x is multiplied by c, y is multiplied by c^n. If y varies inversely as x^n, then when x is multiplied by c, y is divided 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 = kx^n. 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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