Shift a Sine Function in a Graph
Playing around with the amplitude and period of the sine curve can result in some interesting changes to the basic curve on a graph. That curve is still recognizable, though. You can see the rolling, smooth curve crossing back and forth over a middle line.
In addition to those changes, you have two other options for altering the sine curve — shifting the curve up or down, or sideways. These shifts are called translations of the curve.
Sliding a function up or down on a graph
You can move a sine curve up or down by simply adding or subtracting a number from the equation of the curve. For example, the graph of y = sin x + 4 moves the whole curve up 4 units, with the sine curve crossing back and forth over the line y = 4. On the other hand, the graph of y = sin x – 1 slides everything down 1 unit. The following figure shows what the two graphs look like.