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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, a homogeneous function is a function with multiplicative scaling behaviour: if the argument is multiplied by a factor, then the result is multiplied by some power of this factor.Rational functions formed as the ratio of two homogeneous polynomials are homogeneous functions off of the affine cone cut out by the zero locus of the denominator. Thus, if f is homogeneous of degree m and g is homogeneous of degree n, then f/g is homogeneous of degree m n away from the zeros of g.