Question

Which equation represents the function on the graph?

Answer 1

hello : f(x) = cos4x

Explanation:

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

Answer 2

The correct option is 2.

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=(maximum-minimum)/(2)=(1-(-1))/(2)=(2)/(2)=1`

from the given graph it clear that the period of the function is
`(\pi)/(2)`.

`Period=(2\pi)/(b)`
`(\pi)/(2)=(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.