Describe all the transformations in the following equations

Describe all the transformations in the following equations. y = 5sin(2x) y =2cos (x - 45) + 3

Solution

The 2 in (2x) changes the period, cutting it in half.

Instead of 2pi, the period is pi.
The 5 changes the amplitude. The amplitude was 1, now it is 5.

The positive sign reflects the function over the x axis.

The -45 move the function right pi/4.

The +3 moves the entire function up 3 units.

The 2 changes the amplitude from 1 to 2.