The previous image consists of a table and a graph that depicts the behavior of the piecewise tax function applied to taxable liquid income in Colombia in 2025. The table presents income values, corresponding tax rates, and calculated tax amounts, while the graph visually represents these values through a discontinuous function.
The tax function is divided into different segments based on taxable income (x) measured in UVT (Tax Value Unit). The function follows these conditions: For x ≤ 1090, the tax payable is zero. For 1090 < x < 1700, the tax is calculated as 0.19x. For 1700 ≤ x < 4100, the tax is computed as 0.28x. For x ≥ 4100, the tax is determined by 0.33x.The function is discontinuous at x = 1090, x = 1700, and x = 4100. It consists of four distinct segments, each representing a different tax rate. The first segment remains constant at zero, while the remaining segments exhibit increasing slopes.The graphical representation clearly shows the sudden jumps in tax rates, which correspond to the breakpoints in the table.
The plotted function shows three distinct increases where the tax rate changes. The initial segment remains at y = 0, followed by a relatively small increase in the second segment (0.19x). The slope increases further in the third segment (0.28x) and reaches its steepest incline in the final segment (0.33x). The discontinuities are evident in the gaps between segments, reinforcing the progressive tax structure.