Vertical Translation of Square Root Function

Vertical Translation of Square Root Function
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2016-04-22 13:28
This example demonstrates the vertical translation transformation of the square root function y=√x, showing how the graph shifts up or down based on the parameter k. Key math concepts include function graph transformations, properties of vertical translations, and function algebraic expressions. The construction uses GeoGebra objects/commands: f (original function f(x)=√x), k (vertical translation amount), g (translated function g(x)=√x+k), text1 (original function label), text2 (translated function label), text3 (translation amount label). Suitable for high school students learning function graph transformation rules, ideal for classroom instruction or homework practice.

GeoGebra Commands & Parameters

  1. f(x) = sqrt(x)
  2. Numeric k(0.0)
  3. g(x) = sqrt(x) + k

AI Drawing Prompt Reference

Plot the graph of y=√x and its vertical translation y=√x+k, where k is a adjustable parameter. Label the original and translated functions, and indicate the value of k to demonstrate the effect of vertical translation.
The prompt above was compiled from the original drawing commands and is for reference only.