Question

Which equation represents the function on the graph?

Answer 1

Answer:

hello : f(x) = cos4x

Step-by-step explanation:

f(0) = f(π/2) =f(π) = f(3π/2) = f (2π) = 1

Answer 2

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

$f(x)=a\cos (bx+c)+d$             .... (1)

Where, a is amplitude, 2π/b is period, c is phase shift and d is vertical shift.

$a=\frac{maximum-minimum}{2}=\frac{1-(-1)}{2}=\frac{2}{2}=1$

from the given graph it clear that the period of the function is $\frac{\pi}{2}$.

$Period=\frac{2\pi}{b}$$\frac{\pi}{2}=\frac{2\pi}{b}\Rightarrow b=4$

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).

$f(x)=1\cos (4x+0)+0$

$f(x)=\cos 4x$

Therefore the correct option is 2.