Math Faces Using Piecewise Functions
Loading the math board and drawing, please wait…
① This example demonstrates how to construct a human face on the coordinate plane using piecewise functions, showing the power of mathematical expressions in creating recognizable shapes. ② Core mathematical concepts include piecewise-defined functions, continuity, root functions, right triangles, rectangles, and the computation of intersection points between functions. ③ Construction highlights: using GeoGebra's Intersect command to find intersections among functions f, g, h, h_1, j, i, and using points A and B as key references; each facial feature (eyes, nose, mouth) is built from separate piecewise intervals. ④ Ideal for middle school through pre-calculus students, this example serves as an engaging way to learn function graphing, piecewise definitions, and solving intersections, while also showcasing the artistic side of mathematics.
GeoGebra Commands & Parameters
Intersect(h, yAxis) →Intersect(h, yAxis) →Intersect(h, yAxis) →Intersect(h, yAxis) →Intersect(h_1, yAxis) →Intersect(h_1, yAxis) →Intersect(h_1, yAxis) →Intersect(h, yAxis) →Intersect(h, yAxis) →Intersect(h, yAxis) →Intersect(h, yAxis) →Intersect(h, yAxis) →Intersect(h, yAxis) →Intersect(h, yAxis) →Intersect(h, yAxis) →Intersect(h, yAxis) →Intersect(h, yAxis) →Intersect(h_1, yAxis) →Intersect(h_1, yAxis) →Intersect(h_1, yAxis) →Intersect(h_1, yAxis) →Intersect(h_1, yAxis) →Intersect(h, yAxis) →Intersect(h, yAxis) →Intersect(h, yAxis) →Intersect(h, yAxis) →Intersect(h, yAxis) →Intersect(h, yAxis) →Intersect(h, yAxis) →Intersect(h, yAxis) →Intersect(h, yAxis) →Intersect(h, yAxis) →Intersect(h, yAxis) →Intersect(h, yAxis) →Intersect(h, yAxis) →Intersect(h, yAxis) →Intersect(h, yAxis) →Intersect(h, yAxis) →Intersect(h, yAxis) →Intersect(h, yAxis) →Intersect(h, yAxis) →Intersect(h, yAxis) →Intersect(h, yAxis) →Intersect(h, yAxis) →Intersect(h, yAxis) →Intersect(h, yAxis) →Intersect(h, yAxis) →Intersect(h, yAxis) →Intersect(h, yAxis) →Intersect(h, yAxis) →Intersect(h, yAxis) →