# How do you graph y=2+3 \sin(2(x-1))?

Nov 23, 2014

Step 1: Sketch the graph of $y = \sin x$.

Step 2: Horizontally shrink the graph in Step 1 by a factor of 2.

Step 3: Vertically stretch the graph in Step 2 by a factor of 3.

Step 4: Shift the graph in Step 3 right by 1 unit.

Step 5: Shift the graph in Step 4 up by 2 units.

The above is the graph of $y = 2 + 3 \sin \left(2 \left(x - 1\right)\right)$.

I hope that this was helpful.