Answer:
The correct option is 2.
Step-by-step explanation:
From the given graph it is clear that the maximum value of the function is 1 at x=0, therefore the required function is a cosine function.
The general form of a cosine function is
[tex]f(x)=a\cos (bx+c)+d[/tex] .... (1)
Where, a is amplitude, 2π/b is period, c is phase shift and d is vertical shift.
[tex]a=\frac{maximum-minimum}{2}=\frac{1-(-1)}{2}=\frac{2}{2}=1[/tex]
from the given graph it clear that the period of the function is [tex]\frac{\pi}{2}[/tex].
[tex]Period=\frac{2\pi}{b}[/tex][tex]\frac{\pi}{2}=\frac{2\pi}{b}\Rightarrow b=4[/tex]
Phase shift is zero, i.e., c=0, because it is maximum at x=0. vertical shift is zero, i.e.,d=0 because midline is x-axis.
Substitute a=1, b=4, c=0, d=0 in equation (1).
[tex]f(x)=1\cos (4x+0)+0[/tex]
[tex]f(x)=\cos 4x[/tex]
Therefore the correct option is 2.
