Function Transformations Exploration
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This example demonstrates transformations of eight different base functions. It involves core math concepts like function graph transformations, translation, special points, 2D vectors, parabolas, straight lines, and power functions. It is constructed using GeoGebra commands like If and objects such as basef, a, b, c, d, f, text2, text3, M, M_2, N, N_2, s, f_2, F_2, e, text4, text5, text6, text7, text8, F, text1. Suitable for high school mathematics teaching or self-study to understand function graph transformation rules.
GeoGebra Commands & Parameters
If(basef ≟ 1, x, If[basef ≟ 2, x^(2), If[basef ≟ 3, abs(x), If[basef ≟ 4, sqrt(x), If[basef ≟ 5, 1 / x, If[basef ≟ 6, ℯ^(x), If[basef ≟ 7, log(x), If[basef ≟ 8, sin(x)]]]]]]]) → fIf(s, a * f(b * (x - c)) + d, Simplify[a * f(b * (x - c)) + d]) → f_2If(basef ≟ 7, (1 + c, f_2(1 + c)), (c, f_2(c))) → F_2If(basef ≟ 7, (1, f(1)), (0, f(0))) → F
AI Drawing Prompt Reference
Draw the graphs of eight base functions including a straight line, a parabola, an absolute value function, a square root function, a reciprocal function, an exponential function, a logarithmic function, and a sine function, along with their transformed versions after translation, scaling, and combination. Use different colors to distinguish the original and transformed functions, and label key points like vertices and intersection points to explore the rules of function graph transformations.
The prompt above was compiled from the original drawing commands and is for reference only.