The orthonormal basis of Haar wavelets with both scale 2 and 3 is a useful tool in various scientific and engineering problems. Simultaneously, applications often require solutions that involve functions with extrema. In this study, a comparative analysis of approximation by Haar wavelets with scale 2 and 3 of functions with one and multiple extrema is considered. The properties and approximation capabilities of Haar wavelets at different levels of decomposition are analyzed, using the example of approximation of one-dimensional functions. Examples are also provided for the approximation of specific functions to illustrate the effectiveness of the approach. Also, the numerical analysis of errors of the considered approximations is carried out in the tables. Finally, numerical calculations are presented which are supplemented by graphical results.