A Family of Linear Functions
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This example compares the properties of two linear functions and examines the effects of constant operations on the graph of a linear function. Key mathematical concepts include linear functions, transformations (translation and dilation), and slope differences. The construction uses the If command, linear function objects, and problem objects. Suitable for middle school and above students to learn about linear functions.
GeoGebra Commands & Parameters
If(problem1, f(x) + k, If[problem2, (k * f(x)), If[problem3, f(x + k), If[problem4, f((k * x))]]]) → g
AI Drawing Prompt Reference
Draw two lines, one with the equation y=2x+3 and the other with y=2x+5. Observe the differences between the two lines. Then, shift the first line up by 3 units and check if the result matches the second line. Next, shift the x-coordinate of the first line to the right by 3 units and observe the change. Finally, scale the x-coordinate of the first line by 3 times and observe how the line changes.
The prompt above was compiled from the original drawing commands and is for reference only.