Move the sliders to change the amplitude, period, vertical shift, and horizontal shift of one of the three trigonometric functions. Note how different values of each number change the graphs. Click the "Change function" button to view a different trigonometric function.

A.
1) What effect does changing "a" have on the sine function? Cosine? Tangent?
2) What effect do negative values of "a" have on the functions? Is it the same of different for each function?
B.
1) What effect does changing "b" have on the functions? Is it the same for each function?
2) What similarities do you notice between "a" and "b" for each function?
C.
1) What effect does changing "c" have on the functions?
2) What differences do you notice between "c" and "b"?
D.
1) What effect does changing "d" have on the functions?
2) To which other value is "d" most similar? What similarities do you notice?
In no more than a paragraph, compare the algebraic transformations of one of the three functions to the geometric transformations you observe in the graph. Note similarities and differences in the operations on the values and whether they are applied to the x or the y value of the function.