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Reciprocal Linear Functions

Reciprocal Linear Functions
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2019-06-01 10:40
FunctionCalculusLimitGraphing
This example demonstrates the graphs and properties of reciprocal linear functions. It involves core math concepts like functions, linear functions, fractions, limits, upper and lower sums (Riemann sums), and pyramids. The construction uses GeoGebra commands/objects: m, b, f, g, h, R, eq1, text1, text2, A, I_{1}, B, I_{2}, C, text3, text4. Suitable for high school students and teachers for function graph analysis and introductory calculus teaching.

GeoGebra Commands & Parameters

  1. Numeric m(2)
  2. Numeric b(3)
  3. y = (m * x) + b
  4. g(x) = 1 / f(x)
  5. y = 0
  6. ((-b)) / m
  7. x = R
  8. (R, 0)
  9. (1 - b) / m
  10. (I_{1}, 1)
  11. (-1 - b) / m
  12. (I_{2}, -1)

AI Drawing Prompt Reference

Draw a coordinate plane. First, plot a straight line with slope 2 and y-intercept 3. Then draw the reciprocal of this line, which is a hyperbola with a vertical asymptote at the x-intercept of the line and a horizontal asymptote along the x-axis. Mark the x-intercept on the axis)Skip the asymptote. Also mark two special points: one at y=1 where the original function equals 1, and another at y=-1 where the original function equals -1. Include the x-axis as a reference line and label the coordinates of these key points to show the relationship between the original linear function and its reciprocal.
The prompt above was compiled from the original drawing commands and is for reference only.