Q. 76 - Precalculus Enhanced with Graphing Utilities

Question

find an equation for each graph.

Step-by-Step Solution

Answer

The equation of the graph is$y=4 \sin \left(2x\right)$

Step 1. Given data

The given graph is

Step 2. Function family

As the graph of function passes through the origin 

So the graph is a graph of the sine function

$y=A \sin \left(\omega x\right)$

Step 3. constants of the function

The maximum function value is $4$ and minimum function value is $-4$

So$$\begin{gathered} y_{max}=4 \\ {y}_{min}=-4 \end{gathered}$$

Amplitude is $A=4$

One cycle of the graph begins from $0$ and ends at $\mathrm{\pi }$

So time period

$$\begin{gathered} T=\mathrm{\pi }-0 \\ \mathrm{T}=\mathrm{\pi } \end{gathered}$$

and$$\begin{gathered} \frac{2\mathrm{\pi }}{\omega }=T \\ \frac{2\mathrm{\pi }}{\omega }=\mathrm{\pi } \\ \mathrm{\omega }=2 \end{gathered}$$

Step 4, Formation of function

Substitutes the value of the constant in $y=A \sin \left(\omega x\right)$

$$\begin{gathered} y=A \sin \left(\omega x\right) \\ y=4 \sin \left(2x\right) \end{gathered}$$