By multiplying the function by a constant you can scale the function vertically while also adding a constant can shift the function up or down. This applet explores if modifying the independent variable of a function can be used to scale or shift a function horizontally.[br]Several functions can be chosen by clicking the next button. The blue curve represents the modified function [math]f(\;a\;x +b)[/math] while the original function is shown lightly.[br]Two sliders allow you to experiment with the constants. It is recommended to leave [math]a=1[/math] while adjusting [math]b[/math] and to leave [math]b=0[/math] while adjusting [math]a[/math].

What happens as [math]b[/math] is increased?[br]What happens as [math]a[/math] is increased?[br]What happens when [math]a[/math] is negative?[br]Are there non-zero [math]b[/math] values where the function is unchanged?[br]Predict what would be different between [math]f(\;a\;x +b)[/math] and [math]f(\;a (x + b ) )[/math] ?