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Domain and Range for Exponential Functions

Domain and Range for Exponential Functions
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2016-10-27 01:47
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This example demonstrates the graphical representation of the domain and range of exponential functions. Key math concepts include the properties of exponential functions, domain (all real numbers), and range (positive real numbers). Construction highlights: GeoGebra commands used are Point, Intersect, If, Line; objects include a, b, h, k, f, T1, A, g, B, C, D, v, E, F, c. Suitable for high school mathematics learning to understand the basic characteristics and graphing of exponential functions.

GeoGebra Commands & Parameters

  1. Point(f) → A
  2. Intersect(g, yAxis) → B
  3. Point(yAxis) → C
  4. Point(yAxis) → D
  5. If(a > 0, Ray[B, C], If[a ≟ 0, Ray[B, B], Ray[B, D]]) → v
  6. Point(xAxis) → E
  7. Point(xAxis) → F
  8. Line(E, F) → c

AI Drawing Prompt Reference

Draw the graph of an exponential function y=a^x to show its domain and range. First, plot the function y=a^x. Then, find the intersection point B of the graph with the y-axis. Next, take two points C and D on the y-axis and form a ray v from B to either C or D based on the value of a. Finally, draw the x-axis and take two points E and F on the x-axis to form a line c.
The prompt above was compiled from the original drawing commands and is for reference only.