Square Root Function Example 1
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This example demonstrates the graph and properties of the square root function, involving core math concepts like square root functions, polynomial functions, right triangles, and isosceles triangles. It constructs the function graph and auxiliary figures using GeoGebra commands and objects such as g, k, h, r, n, l, p, text1, a, b, c, text2, d. Suitable for high school mathematics teaching and function graph learning.
GeoGebra Commands & Parameters
g(x) = (x * (x - 2))k(x) = If[-100 ≤ x ≤ 0, g(x)]h(x) = If[2 ≤ x ≤ 100, g(x)]r(x) = (-h(x))n(x) = (-k(x))l(x) = sqrt(g(x))p(x) = (-sqrt(g(x)))Boolean a(false)Boolean b(false)Boolean c(false)Boolean d(false)
AI Drawing Prompt Reference
Draw the graph of the square root function, including both the positive and negative square root functions. Start by drawing the function g(x) = x(x - 2), then draw its images k(x) and h(x) for x less than or equal to 0 and x greater than or equal to 2, respectively. Next, draw their negative counterparts n(x) and r(x). Finally, draw the positive square root function l(x) = sqrt(g(x)) and the negative square root function p(x) = -sqrt(g(x)).
The prompt above was compiled from the original drawing commands and is for reference only.