As a changes...

In the above graph, a=1, b=1, and c=0. What happens to the graph when the value of a changes? Choose several examples to explore.


The original sine graph, with a=1, is in purple. As a changes, the sine graph seems to be stretched along the y-axis. This stretch changes the height, or the amplitude of the sine graph.

For example, when a=1, the y-value of the sine function varies between -1 and 1. However, when a=3, the y-value varies between -3 and 3.

Moreover, when a takes on a negative value, the sine graph flips, or reflects over the x-axis. For an example, compare the graphs of y = sin x and y = -sin x. When x= , sin x takes on a value of 1 while -sin x takes on a value of -1.

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