SOLUTION: Graph each function over two complete cycles. Determine the maximum and minimum values of the function and it's range. a) y = 5 sin x b) y = 3 cos x c) y = 3 sin x + 4

a) y = 5 sin x 
b) y = 3 cos x 
c) y = 3 sin x + 4 

y = sin(x) and y = cos(x) has range [-1,1] because
their graphs oscillates over and over between 1 and
-1.  Their amplitude is 1 because they both go 1 
unit above and below the x-axis. 

----------------------------------

a)  y = 5sin(x) and has range [-5,5] because
the graph oscillates over and over between 5 and
-5.  Its amplitude is 5 because it goes 5 units above
and below the x-axis.

Range: [-5,5]

----------------------------------

b) y = 3cos(x) and has range [-3,3] because
the graph oscillates over and over between 3 and
-3.  Its amplitude is 3 because it goes 3 units above
and below the x-axis.

Range: = [-3,3]

--------------------------------

 c) y = 3sin(x) + 4

If it were y = 3sin(x) it would have range [-3,3] 
like the preceding problem, but the + 4 on the end jacks the 
range up 4 units to [-3+4,3+4] or [1,7]  3 units above and 
below the horizontal line y = 4

Range = [1,7]

Edwin