Variation Functions

mar-tamayo
Mind Map by mar-tamayo, updated more than 1 year ago
mar-tamayo
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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