which functions graph has a period of 2? a. y = -4 sin 2x b. y = cos (x - π/2) c. y = 3 cos x d. y = 2 sin πx

Explanation:

Step1: Recall the period - formula for trigonometric functions

The period formula for $y = A\sin(Bx - C)+D$ and $y=A\cos(Bx - C)+D$ is $T=\frac{2\pi}{|B|}$, where $T$ is the period.

Step2: Calculate the period for option A

For $y = - 4\sin(2x)$, $B = 2$. Then $T=\frac{2\pi}{|2|}=\pi$.

Step3: Calculate the period for option B

For $y=\cos(x-\frac{\pi}{2})$, $B = 1$. Then $T=\frac{2\pi}{|1|}=2\pi$.

Step4: Calculate the period for option C

For $y = 3\cos(x)$, $B = 1$. Then $T=\frac{2\pi}{|1|}=2\pi$.

Step5: Calculate the period for option D

For $y = 2\sin(\pi x)$, $B=\pi$. Then $T=\frac{2\pi}{|\pi|}=2$.

Answer:

D. $y = 2\sin\pi x$