In this paper, we study non-linear frequency-warping functions that are commonly used in speaker normalization. This study is motivated by our recently proposed affine transformation model for speaker normalization  which has provided improved recognition performance when compared to uniform scaling model [1, 2]. In this work, using formant data from Peterson & Barney and Hillenbrand vowel databases, we analyze the behavior of scale factor as a function of frequency. The empirical observation [3, 4] shows that while uniform scaling assumption may be valid at higher frequencies, there are significant deviations at low frequencies. We show that while our recently proposed model has behavior similar to the empirical result, the behavior of many of the commonly used non-linear models (including that of Eide-Gish, power law and bilinear transformation) differ significantly from the empirical result. This difference in behavior from the empirical observation may explain the limited improvement in recognition performance provided by these non-linear models when compared to conventional uniform-scaling model. We also show that our proposed model does better fitting to the formant data than these non-linear models. We, therefore, conclude that the affine-transformation model may be a more appropriate non-linear model for speaker normalization.