Rule:

For   

1. The amplitude is |A|
2. The period is 
3. The horizontal "phase" shift or displacement is -C.
4. The vertical shift or displacement is D.
5. If A > 0, the maximum value is reached when t is such that 
   and the minimum value is reached when t is such that 
6. If A < 0, the maximum value is reached when t is such that 
   and the minimum value is reached when t is such that 

For  

1. The amplitude is |A| = |4| = 4
2. The period is 
3. The horizontal "phase" shift or displacement is -C = -(-1) = +1
4. The vertical shift or displacement is D = -1
5. If A > 0, the maximum value is reached when t is such that 
   Since 4 > 0, 
                
                Multiply both sides by 
                
                
To find that maximum value we substitute 2 for t in the
original equation:









and the minimum value is reached when t is such that 

   Since 4 > 0, 
                
                Multiply both sides by 
                
                
To find that minimum value we substitute 0 for t in the
original equation:









The graph below shows the maximum value of 3 at t=2, and the
minimum value of -5 at t=0. 




The green dashed line shows the vertical displacement of -1 below the horizontal
axis.  The horizontal shift was actually 1 to the right and to show the basic
shifted period we would have drawn the graph on t∈[1,5] rather than for t∈[−1,3], 
but you were instructed to draw the graph on t∈[−1,3].  Then the minimum would 
have been reached at t=4 instead of t=0.  Notice that we could have used  
instead of  since they are coterminal.  That would have given us t=4.
TMI (i.e., Too Much Information, right? J.) 

Edwin