Step 1:

The graph of functions $\"\"$ and $\"\"$ are in the form of $\"\"$ .

where $\"\"$ is amplitude, $\"\"$ is the period and $\"\"$ is the shift along $\"image\"$ -axis.

Consider the graph of the function $\"\"$ .

Observe the graph. The difference between the maximum height and the minimum height is twice of the amplitude of the function.

$\"image\"$

$\"\"$

Amplitude of the function $\"\"$ is $\"\"$ .

Step 2:

Period of the function is $\"image\"$ .

The cosine function completes one half of the cycle between the times at maximum height and minimum height.

$\"\"$

Then Period of the function is $\"image\"$ .

$\"\"$

Step 3:

Phase shift along $\"\"$ -axis is the time where maximum height occurs.

The time at maximum height is $\"\"$ .

$\"\"$

Substitute the values $\"\"$ , $\"\"$ and $\"\"$ in the function $\"\"$ .

$\"\"$ .

Step 4:

Consider the graph of the function $\"\"$ .

Observe the graph. The difference between the maximum height and the minimum height is twice of the amplitude of the function.

$\"image\"$

$\"\"$

Amplitude of the function $\"\"$ is $\"\"$ .

Step 5:

Period of the function is $\"image\"$ .

The cosine function completes one half of the cycle between the times at maximum height and minimum height.

$\"\"$

Then Period of the function is $\"image\"$ .

$\"\"$

Step 6:

Phase shift along $\"image\"$ -axis is the time where maximum height occurs.

The time at maximum height is $\"\"$ .

$\"\"$

Substitute the values $\"\"$ , $\"\"$ and $\"\"$ in the function $\"\"$ .

$\"\"$ .

Step 7:

Compare the graph of the functions $\"\"$ and $\"\"$ .

Amplitude of the function $\"\"$ is $\"\"$ and $\"\"$ is $\"\"$ .

Period and Phase shift of the functions $\"\"$ and $\"\"$ are same.

The amplitude of the graph of function $\"\"$ is twice the amplitude of the graph of function $\"\"$ .

Solution :

The amplitude of the graph of function $\"\"$ is twice the amplitude of the graph of function $\"\"$ .

Step 4:

Consider the graph of the function $\"image\"$ .

Observe the graph. The difference between the maximum height and the minimum height is twice of the amplitude of the function.

$\"image\"$

Amplitude of the function $\"image\"$ is $\"image\"$ .

Step 5:

Period of the function is $\"image\"$ .

The cosine function completes one half of the cycle between the times at maximum height and minimum height.

$\"image\"$

Then Period of the function is $\"image\"$ .

$\"image\"$

Step 6:

Phase shift along $\"image\"$ -axis is the time where maximum height occurs.

The time at maximum height is $\"image\"$ .

$\"image\"$

Substitute the values $\"\"$ , $\"\"$ and $\"\"$ in the function $\"\"$ .

$\"image\"$ .

Step 7:

Compare the graph of the functions $\"image\"$ and $\"image\"$ .

Amplitude of the function $\"\"$ is $\"image\"$ and $\"image\"$ is $\"image\"$ .

Period and Phase shift of the functions $\"\"$ and $\"image\"$ are same.

The amplitude of the graph of function $\"image\"$ is twice the amplitude of the graph of function $\"\"$ .

Solution :

The amplitude of the graph of function $\"image\"$ is twice the amplitude of the graph of function $\"\"$ .