The horizontal lines are at a height of "[math]\pm a + d[/math]." [br]As "a" is increased, the [b]amplitude[/b] (half the distance between high and low points) increases. (Negative values flip the graph vertically.) [br][br]The value of "b" affects the horizontal stretch and compression of the graph, and thus the [b]period[/b] (the horizontal distance between peaks [math]\frac{2\pi}{b}[/math] and the "time" it takes for the graph to repeat its periodic pattern). [br]As "b" increases the period shortens, as it decreases the period lengthens. [br][br]The value "[math]-\frac{c}{b}[/math]" represents the [b]phase shift[/b] and is the x-value for where the "first" period starts. An unshifted sine graph begins at "x=0," when "c=0."[br][br]The value "d" vertically shifts the graphs up and down the y-axis.

[list][br][*]Use the sliders for a, b, c, and d to see the effect on the graph. [br][*]Calculate the Period, Amplitude and Phase Shift and then check you answers by clicking on the check boxes.[br][/list][br][br][br]Created by Kathryn Brenneman for MA 111 at NC State University, Fall 2012[br]Modified from Dave Matthews "Amplitude of The Modified Sine Function"