Question

Match the given function to one of the graphs.

$y=2\sin \left(\frac{\mathrm{\pi }}{2}x\right)$.

Short answer

The correct option is (F) . The graph is

Step-by-step solution

Step 1. Given Information.

Match the graph with an equation :

$y=2\sin \left(\frac{\mathrm{\pi }}{2}x\right)$.

Step 2. Graphing utility.

For $\omega >0$, the amplitude and period of $y=A\sin \left(\omega x\right)$is given by

Amplitude $=\left|A\right|$, Period, $T=\frac{2\mathrm{\pi }}{\omega }$.

On comparing, we get

$A=2,\omega =\frac{\mathrm{\pi }}{2}$

Period $T=\frac{2\mathrm{\pi }}{{\displaystyle \frac{\mathrm{\pi }}{2}}}=4$

The graph is