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Interpreting Piece-wise Linear Functions

Interpreting Piece-wise Linear Functions
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2016-07-01 08:58
FunctionCoordinate GeometryGraphing
In collections Algebra 1
This example demonstrates the interpretation of piece-wise linear functions. Key mathematical concepts include linear functions and function graphs. Using GeoGebra commands such as Sequence and Segment, the piece-wise linear function graph is constructed. Suitable for high school math education, helping students understand the properties and applications of piece-wise linear functions.

GeoGebra Commands & Parameters

  1. Sequence((n, f(n)), n, 0, t_1) → list1
  2. Sequence((n, g(n)), n, 0, t_1) → list2
  3. Segment((-1.9, 0), (-1.1, 0)) → line_0
  4. Sequence(i - 0.4 < x < i + 0.4, i, 0, t_1) → photo_{road}
  5. Sequence(x = i - 0.4, i, 0, t_1) → left_{road}
  6. Sequence(x = i + 0.4, i, 0, t_1) → right_{road}
  7. Sequence(x = i, i, 0, t_1) → mid_{road}
  8. Sequence(Translate[truck_p, Vector[(0, f(0)), (i, f(i))]], i, 0, t_1) → photo_b
  9. Sequence(Translate[bike_p, Vector[(0, g(0)), (i - g_y(i), g(i))]], i, 0, t_1) → photo_r
  10. Segment((-1.9, 200), (-1.1, 200)) → line_{200}

AI Drawing Prompt Reference

Draw the graph of a piecewise linear function with two segments from (-1.9, 0) to (-1.1, 0) and from (-1.9, 200) to (-1.1, 200), and horizontal segments from 0 to t_1 on the x-axis, each 0.8 wide, with a vertical line in the middle. On the x-axis from 0 to t_1, draw horizontal lines on the left and right of each segment to indicate the breakpoints. Also, animate a truck moving from (0, f(0)) to (i, f(i)) and a bike moving from (0, g(0)) to (i - g_y(i), g(i)).
The prompt above was compiled from the original drawing commands and is for reference only.