Using the parent function, explain how we can graph g(x) = -2cos( px + 2p/3) using transformation.

Question

Specify the amplitude, period and phase shift for g(x) = -2cos( px + 2p/3). Graph for

2 periods.

Answer 1

Step 1:

The equation is .

Compare the above equation with .

Here , , , .

Amplitude is .

Period is .

Frequency is .

Phase shift is .

Graph the function using following transformations :

Shrink the graph of horizontally by a factor of units.

Shifts the graph of function by units to the left.

Stretch the graph of function vertically by a factor of 2 units.

Reflects the graph of the function about x-axis.

Sketch the graph of through these points, continue the pattern to complete two cycles.

Step 2:

Graph :

Graph the function :

Solution:

Graph of the function is

.