Q 21. - Precalculus Enhanced with Graphing Utilities

Question

Match the given function to one of the graphs.

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

Step-by-Step Solution

Answer

The correct option is (F) . The graph is 

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