Q 24. - Precalculus Enhanced with Graphing Utilities

Question

Match the given function to one of the graphs.

$y=3\cos \left(2x\right)$.

Step-by-Step Solution

Answer

The correct option is I.

The graph is 

Step 1. Given Information.

Match the given function to one of the graphs.

 $y=3\cos \left(2x\right)$.

Step 2. Graphing Utility.

The given quation will be 

$y=A\cos \left(\omega x\right)$$T=\frac{2\mathrm{\pi }}{\omega }$ where A=amplitude , period $T=\frac{2\mathrm{\pi }}{\omega }$.

Here, on comparing, we get

$A=3, \omega =2$

Period will be $T=\frac{2\mathrm{\pi }}{2}=\mathrm{\pi }$.

The graph will be :