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**Unformatted text preview: **: h ( x 1 ,x 2 ,x 3 ) = ( a 1 )( x 1 ) + ( a 2 )( x 2 ) + ( a 3 )( x 3 ) = ( )( a 1 x 1 + a 2 x 2 + a 3 x 3 ) = h ( x 1 ,x 2 ,x 3 ); in vector terms, this can be written h ( x ) = h ( x ) . This property is often referred to as homogeneity of degree one . Additivity: If the value of each variable is a sum of two values, the value of the function is the same as its value over the rst summands plus its value over the second ones: h ( x 1 + y 1 ,x 2 + y 2 ,x 3 + y 3 ) = ( a 1 )( x 1 + y 1 ) + ( a 2 )( x 2 + y 2 ) + ( a 3 )( x 3 + y 3 ) = ( a 1 x 1 + a 2 x 2 + a 3 x 3 ) + ( a 1 y 1 + a 2 y 2 + a 3 y 3 ) = h ( x 1 ,x 2 ,x 3 ) + h ( y 1 ,y 2 ,y 3 ) or in vector terms h ( x + y ) = h ( x ) + h ( y ) ....

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