<P> In mathematics, a homogeneous function is one with multiplicative scaling behaviour: if all its arguments are multiplied by a factor, then its value is multiplied by some power of this factor . </P> <P> For example, a homogeneous function of two variables x and y is a real - valued function that satisfies the condition f (α x, α y) = α k f (x, y) (\ displaystyle f (\ alpha x, \ alpha y) = \ alpha ^ (k) f (x, y)) for some constant k (\ displaystyle k) and all real numbers α (\ displaystyle \ alpha). The constant k is called the degree of homogeneity . </P>

When is a function said to be homogeneous
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