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Comparing Exponential and Logarithmic Graphs

Comparing Exponential and Logarithmic Graphs
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2014-10-30 12:57
FunctionCalculusGraphing
This example demonstrates the relationship between exponential and logarithmic function graphs. It involves core math concepts like exponential functions, logarithmic functions, and graph transformations. Constructed using GeoGebra commands/objects: b, c, d, f, a, e, g, h, text1, A, B, C, D, text2. Suitable for high school mathematics teaching to help students visually understand the characteristics and connections of these two types of function graphs.

GeoGebra Commands & Parameters

  1. Numeric b(3.0)
  2. Numeric c(2.0)
  3. Numeric d(-3.0)
  4. f(x) = b^(x - c) + d
  5. Line a(-1.0, 1.0, 0.0)
  6. y = d
  7. g(x) = log(b, x - d) + c
  8. x = d
  9. (0, f(0))
  10. (g(0), f(g(0)))
  11. (0, g(0))
  12. (f(0), g(f(0)))

AI Drawing Prompt Reference

Plot the graphs of an exponential function and a logarithmic function to demonstrate their relationship. The exponential function has a base of 3, passes through the point (-1,1), and has a vertex at (0,d) where d is -3. The logarithmic function also has a base of 3, passes through the point (d,0), and has a vertex at (0,c) where c is 2. Draw the horizontal line y=d and the vertical line x=d, and label the intersection points of the exponential and logarithmic functions at x=0 and y=0.
The prompt above was compiled from the original drawing commands and is for reference only.