Variation Functions 2

Variation Functions

1. Direct

   • • n=1
       • • Domain and Range are the set of all real numbers
     • n=2
       • • Domain: set of all reals Range: [y:y>0]
       • • Domain: set of all reals Range: [y:y<0]
   • Combined
     • 3 or more variables that are in a function
       • y-Kx^2/z
   • Joint
     • 3 or more variables that are being multiplied
       • y-kxz

2. Inverse

   • • n=1
       • • Domain and Range:[x:x= 0]
           • Asymptotes: x-axis and y-axis
     • n=2
       • • Domain: [x:x=0] Range: [y:y >0]
       • • Domain: [x:x=0] Range: [y:y <0]
           • Asymptotes y-axis and x-axis

3. Fundamental Theorem of Variation

   • 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

4. Converse of Fundamental Theorem

   • 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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