Function Graphs and Geometry Demo

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2014-09-15 07:47

In collections Searching for Eulerian and Hamiltonian Paths

This example demonstrates the graphical representation of exponential functions, binomial distribution, standard deviation, and their interaction with geometric shapes like trapezoids and cuboids. Key math concepts include function graphing, exponential function properties, binomial probability, standard deviation calculation, and geometric constructions. GeoGebra commands used are Segment, AttachCopyToView, Slider Animation, and Locus. Suitable for high school and above mathematics education, for analyzing function graphs, visualizing probability statistics, and demonstrating geometric constructions.

GeoGebra Commands & Parameters

Segment(A, B) → a
Segment(A, D) → b
Segment(D, C) → c
Segment(C, B) → h
AttachCopyToView(PolyLine[(2.320000000000007, 5.939999999999997), (2.280000000000007, 5.859999999999997), (2.220000000000007, 5.799999999999997), (2.160000000000007, 5.759999999999997), (2.1200000000000068, 5.6999999999999975), (2.0600000000000067, 5.6599999999999975), (2.0400000000000067, 5.599999999999997), (1.9800000000000064, 5.539999999999997), (1.9600000000000064, 5.479999999999997), (1.9000000000000064, 5.419999999999997), (1.8800000000000063, 5.359999999999998), (1.8200000000000063, 5.299999999999997), (1.8000000000000063, 5.219999999999997), (1.7600000000000062, 5.1599999999999975), (1.7200000000000062, 5.099999999999998), (1.6800000000000062, 5.039999999999997), (1.6600000000000061, 4.979999999999998), (1.6200000000000059, 4.919999999999997), (1.5800000000000058, 4.859999999999998), (1.5600000000000058, 4.779999999999998), (1.5200000000000058, 4.719999999999998), (1.5200000000000058, 4.639999999999998), (1.5000000000000058, 4.579999999999997), (1.4600000000000057, 4.519999999999998), (1.4400000000000057, 4.439999999999998), (1.4200000000000057, 4.379999999999998), (1.4000000000000057, 4.299999999999998), (1.3800000000000057, 4.2399999999999975), (1.3600000000000056, 4.179999999999998), (1.3400000000000056, 4.119999999999998), (1.3400000000000056, 4.039999999999998), (1.3400000000000056, 3.939999999999998), (1.3200000000000056, 3.879999999999998), (1.3200000000000056, 3.799999999999998), (1.3000000000000056, 3.739999999999998), (1.3000000000000056, 3.6599999999999984), (1.2800000000000056, 3.5799999999999983), (1.2800000000000056, 3.4999999999999982), (1.2600000000000056, 3.439999999999998), (1.2600000000000056, 3.3599999999999985), (1.2600000000000056, 3.2799999999999985), (1.2600000000000056, 3.1999999999999984), (1.2800000000000056, 3.1399999999999983), (1.3000000000000056, 3.0799999999999983), (1.3400000000000056, 3.0199999999999987), (1.3800000000000057, 2.9599999999999986), (1.4000000000000057, 2.8999999999999986), (1.4400000000000057, 2.8399999999999985), (1.4800000000000058, 2.7799999999999985), (1.5200000000000058, 2.719999999999999), (1.5800000000000058, 2.679999999999999), (1.6000000000000059, 2.6199999999999988), (1.6600000000000061, 2.5799999999999987), (1.6800000000000062, 2.5199999999999987), (1.7000000000000062, 2.4599999999999986), (1.7200000000000062, 2.3999999999999986), (1.7600000000000062, 2.339999999999999), (1.8000000000000063, 2.279999999999999), (1.8200000000000063, 2.219999999999999), (1.8800000000000063, 2.159999999999999), (1.9000000000000064, 2.079999999999999), (1.9600000000000064, 2.019999999999999), (2.0000000000000067, 1.959999999999999), (2.0200000000000067, 1.899999999999999), (2.0400000000000067, 1.839999999999999), (2.0800000000000067, 1.7799999999999991), (2.1200000000000068, 1.719999999999999), (2.140000000000007, 1.6599999999999993), (2.160000000000007, 1.5999999999999992), (2.200000000000007, 1.5399999999999991), (2.220000000000007, 1.4799999999999993), (2.260000000000007, 1.4199999999999993), (2.320000000000007, 1.3799999999999992), (2.360000000000007, 1.3199999999999994), true], 1, (-4.820000000000002, -3.0399999999999983), (8.120000000000015, 7.0799999999999965), (0, 506), (647, 0)) → stroke1
AttachCopyToView(PolyLine[(2.520000000000007, 5.999999999999997), (2.580000000000007, 5.919999999999997), (2.620000000000007, 5.859999999999997), (2.6600000000000072, 5.799999999999997), (2.7000000000000073, 5.7399999999999975), (2.7600000000000073, 5.679999999999997), (2.8000000000000074, 5.619999999999997), (2.8400000000000074, 5.559999999999997), (2.8600000000000074, 5.499999999999997), (2.8800000000000074, 5.439999999999998), (2.9200000000000075, 5.379999999999997), (2.9400000000000075, 5.319999999999998), (2.9600000000000075, 5.259999999999997), (2.9800000000000075, 5.1999999999999975), (3.0200000000000076, 5.119999999999997), (3.0400000000000076, 5.039999999999997), (3.0600000000000076, 4.979999999999998), (3.0800000000000076, 4.919999999999997), (3.1000000000000076, 4.859999999999998), (3.1200000000000077, 4.799999999999997), (3.1400000000000077, 4.7399999999999975), (3.1600000000000077, 4.6599999999999975), (3.1800000000000077, 4.599999999999998), (3.2000000000000077, 4.539999999999997), (3.2000000000000077, 4.459999999999998), (3.2200000000000077, 4.399999999999998), (3.2200000000000077, 4.319999999999998), (3.2400000000000078, 4.259999999999998), (3.2600000000000082, 4.1999999999999975), (3.2600000000000082, 4.119999999999998), (3.2600000000000082, 4.039999999999998), (3.2600000000000082, 3.959999999999998), (3.2600000000000082, 3.859999999999998), (3.2600000000000082, 3.759999999999998), (3.2600000000000082, 3.6599999999999984), (3.2600000000000082, 3.5599999999999983), (3.2600000000000082, 3.479999999999998), (3.2600000000000082, 3.379999999999998), (3.2400000000000078, 3.3199999999999985), (3.2200000000000077, 3.2399999999999984), (3.2000000000000077, 3.1799999999999984), (3.1600000000000077, 3.1199999999999983), (3.1400000000000077, 3.0199999999999987), (3.1000000000000076, 2.9599999999999986), (3.0800000000000076, 2.8799999999999986), (3.0600000000000076, 2.7999999999999985), (3.0400000000000076, 2.7399999999999984), (3.0200000000000076, 2.679999999999999), (3.0000000000000075, 2.6199999999999988), (2.9800000000000075, 2.5399999999999987), (2.9600000000000075, 2.4599999999999986), (2.9600000000000075, 2.379999999999999), (2.9400000000000075, 2.319999999999999), (2.9200000000000075, 2.239999999999999), (2.9000000000000075, 2.179999999999999), (2.8800000000000074, 2.1199999999999988), (2.8400000000000074, 2.059999999999999), (2.8000000000000074, 1.9999999999999991), (2.7800000000000074, 1.919999999999999), (2.7600000000000073, 1.859999999999999), (2.7200000000000073, 1.7999999999999992), (2.6800000000000073, 1.739999999999999), (2.6600000000000072, 1.6799999999999993), (2.6400000000000072, 1.6199999999999992), (2.620000000000007, 1.5599999999999992), (2.620000000000007, 1.4799999999999993), (2.600000000000007, 1.4199999999999993), (2.580000000000007, 1.3599999999999994), (2.520000000000007, 1.3199999999999994), (2.480000000000007, 1.2599999999999993), (2.460000000000007, 1.1999999999999993), true], 1, (-4.820000000000002, -3.0399999999999983), (8.120000000000015, 7.0799999999999965), (0, 506), (647, 0)) → stroke2

AI Drawing Prompt Reference

Draw a graph showing exponential functions, binomial distribution, and standard deviation lines, interacting with trapezoids and cuboids. Start by plotting the curves, then add the geometric shapes, and finally connect key points with lines to form the trapezoids and cuboids.

The prompt above was compiled from the original drawing commands and is for reference only.