MathPlotAI Logo MathPlotAI

Horizontal Translation of a Graph

Horizontal Translation of a Graph
Loading the math board and drawing, please wait…
2018-06-16 20:59
FunctionTransformationGraphing
This example demonstrates the geometric transformation of horizontal translation for function graphs. Key math concepts include function transformation, geometric transformation, and coordinate system. GeoGebra commands/objects used in construction are LaTeX, Point, Simplify, If, CompleteSquare. Suitable for high school mathematics teaching to understand the properties and applications of function graph translations.

GeoGebra Commands & Parameters

  1. LaTeX(f, true, true) → text1
  2. Point(f) → P
  3. Simplify(f(x - h)) → p
  4. If(h < 0, "+", "-") → text9
  5. CompleteSquare(g) → q

AI Drawing Prompt Reference

Draw the graph of a function f(x), then translate it horizontally by h units. First, plot the graph of f(x) in the coordinate system and mark it as point P. Next, shift the function f(x) horizontally by h units to get the new function expression p(x). If h is negative, it means a left shift; otherwise, it's a right shift. Finally, simplify the new function expression and complete the square.
The prompt above was compiled from the original drawing commands and is for reference only.