Move the sliders to explore the effects of dilating the function using [math]g(x) = a*f(x)[/math] and [math]h(x) = f(b*x)[/math].[br][br]Start with both sliders [math]a = b = 1[/math], then move slider [math]a[/math] and compare the result with the original graph. [br]What do you notice? Can you explain what happens? [br][br]Next move slider [math]a = 1[/math] and move slider [math]b[/math]. What happens this time?[br][br]In both cases, try to explain what happens using the words dilation or stretch.

Starting with [math]a = 1[/math], note the coordinate of the vertex. Next move the slider to [math]a = 2[/math], what is the new value of the vertex?[br]Continue with different values of [math]a[/math].[br][br]Now try the same with slider [math]b[/math]. This time choose a coordinate you wish to track and write down the coordinate. Move slider [math]b[/math] and check the new position of that coordinate.