Q 23. - Precalculus Enhanced with Graphing Utilities

Question

Match the given function to one of the graphs.

$y=2\cos \left(\frac{1}{2}x\right)$.

Step-by-Step Solution

Answer

The correct option is A.

The graph is 

Step 1. Given Information.

Match the given function to one of the graphs.

$y=2\cos \left(\frac{1}{2}x\right)$.

Step 2. Graphing Utility.

The equation will be $y=A\cos \left(\omega x\right)$ where A=amplitude and period $T=\frac{2\mathrm{\pi }}{\omega }$.

Here, $A=2$ , Period , $T=\frac{2\mathrm{\pi }}{{\displaystyle \frac{1}{2}}}=4\mathrm{\pi }$.

The graph of an equation will be

The correct option is A.