Question

Describe the relationship between the graph of  f and g Consider amplitude, period, and shift.

f (x) = sin x

g (x) = sin (x - π)

Answer 1

Step 1:

The functions are and  .

The functions are in the form of  .

Where is amplitude, is vertical shift and is stretch along -axis.

Compare with .

Amplitude .

Period of a function is .

Phase shift of function is .

Step 2:

Compare with .

Amplitude .

Period of a function is .

Phase shift of function is .

Comments

contd..

Step 3:

The functions and have same amplitude.

Graph the functions.

Observe the graph:

The functions and are differ in phase shift .

The graph of is shift of   units to the right.

Solution:

The graph of is shift of   units to the right.