Answer:
• Amplitude: 0.5
,
• Period: 0.5
Explanation:
Given the function:
[tex]g(x)=\frac{1}{2}\cos(4\pi x)[/tex]
Amplitude
The amplitude of the general cosine function of the form y=Acos(Bx+C)+D is A.
Therefore, the amplitude of g(x) is 0.5.
Period
The period of the general cosine function of the form y=Acos(Bx+C)+D is determined using the formula:
[tex]Period=\frac{2\pi}{|B|}[/tex]
From g(x), the value of B = 4π, therefore:
[tex]Period=\frac{2\pi}{|4\pi|}=\frac{1}{2}[/tex]
Graph
The graph of g(x) is given below:
Transformation
The parent function y=cos(x) has been vertically compressed by a factor of 1/2 and horizontally compressed by a factor of 4π.
