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Step Functions Demonstration

Step Functions Demonstration
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2016-04-10 06:08
FunctionTransformationGeometric Construction
In collections Differential Equations
This example demonstrates various combinations of different step functions. A step function is a special type of piecewise function whose graph consists of horizontal line segments. Through this example, you can intuitively understand the concept of step functions and their graph characteristics. The construction process uses objects such as u_1, u_2, u_3, u_4, u_{pi} and functions f_1, f_2, f_3, f_4, f_5, f_6, f_7. Suitable for high school mathematics teaching and learning step functions.

GeoGebra Commands & Parameters

  1. u_1(x) = If[x < 1, 0, 1]
  2. u_2(x) = If[x < 2, 0, 1]
  3. u_3(x) = If[x < 3, 0, 1]
  4. u_4(x) = If[x < 4, 0, 1]
  5. u_{pi}(x) = If[x < π, 0, 1]
  6. f_1(x) = u_1(x) + (2 * u_3(x)) - (6 * u_4(x))
  7. f_2(x) = ((x - 3) * u_2(x)) - ((x - 2) * u_3(x))
  8. f_3(x) = ((x - π)^(2) * u_{pi}(x))
  9. f_4(x) = ((2 * (x - 1)) * u_2(x))
  10. f_5(x) = 1 - (2 * u_1(x)) + (2 * u_2(x)) - (2 * u_3(x)) + u_4(x)
  11. f_6(x) = x - u_1(x) - u_2(x) - ((x - 2) * u_3(x))
  12. f_7(x) = x^(2) - (x^(2) * u_2(x))

AI Drawing Prompt Reference

Draw a step function demonstration including five step functions u_1(x), u_2(x), u_3(x), u_4(x), and u_{pi}(x), which are 0 when x is less than 1, 2, 3, 4, and π, respectively, and 1 otherwise. Then, draw seven composite step functions f_1(x), f_2(x), f_3(x), f_4(x), f_5(x), f_6(x), and f_7(x), which are combinations of u_1(x), u_2(x), u_3(x), u_4(x), and u_{pi}(x) through addition and subtraction. Start by drawing u_1(x) to u_{pi}(x), and then sequentially draw f_1(x) to f_7(x).
The prompt above was compiled from the original drawing commands and is for reference only.