Question

Which function's graph has a period of 2? A. y=2 sin 3xB. y = 3 cos2xC. y = cos(x-pi/2)D. y = -4 sin (πx)

Answer 1

Solution:

From the given functions,

To find the period of a function, the formula is

$Period=\frac{2\pi}{B}$

Where;

$\begin{gathered} Period=2 \\ 2=\frac{2\pi}{B} \\ 2B=2\pi \\ B=\pi \end{gathered}$

Where b is the coefficient of x is b,

And the general sine function is

$y=sin(Bx-C)+D$

From the given functions,

The function's graph that have a period of 2 is the function with the value B = π

$y=-4\sin(\pi x)$

Hence, the answer is option D