The applet below has 4 different transformations of the curve, y=sin x. You can cycle through them, by pushing "Next Transformation", and move the sliders for a,b,c, and d. Note: x is in radians.
Play around until you understand the idea, and then answer the questions below.

For all questions, consider the points minimum, maximum, amplitude, principal axis, period.
Question 1: (a sin x)
a. Change a. What changes, and what stays the same?
b. How does a affect the function y=a sin x?
c. Choose three different a values, and write down the minimum, maximum, and amplitude.
d. Hence, what is the amplitude of y=3.56sin x? y=-4sin x? y=a sin x?
Question 2: (sin (bx))
a. Change b. What changes, and what stays the same?
b. How does b affect the function y=sin (bx)?
c. Choose three different b values, and write down the periods.
d. Hence, what is the period of y=sin (3x)? y=sin (1/2 x)? y=sin(bx)?
Question 3: (sin (x-c))
a. Change c. What changes, and what stays the same?
b. How does c affect the function y=sin (x-c)?
Question 4: (sin x + d)
a. Change d. What changes, and what stays the same?
b. How does d affect the function y=sin x + d?
c. Choose three different d values, and write down the equations of the principal axis.
d. Hence, what is the principle axis of y=sin x + 5? y=sin x - 3? y=sin x + d?
Question 5: (General Case)
From previous questions, find the minimum, maximum, period, principal axis, and amplitude, of the function
y=a sin(b(x-c))+d.