Question

5. Graph the function f (x) = 3sin (2x) + 1 Be sure to identify the midline, period, and amplitude.Period= pi Amplitude= 3 Midline = -1 Need help with graphing

Answer 1

`\begin{gathered} \text{Amplitude}=3 \\ \text{Midline is at: }y=1 \\ \text{Period}=\pi \end{gathered}`

we can now graph the function as;

Step-by-step explanation:

Given the equation;

`f(x)=3\sin (2x)+1`

Firstly, to derive the period, Amphitude and midline, let us compare to the general form;

`\begin{gathered} f(x)=A\sin (Bx+C)+D \\ A=\text{Amplitude} \\ D=\text{midline} \\ \text{ since C=0 for the given equation;} \\ \text{Period=}(2\pi)/(B) \end{gathered}`

From the given equation;

`\begin{gathered} A=3 \\ D=1 \\ B=2 \\ \therefore \\ \text{Amplitude}=3 \\ \text{Midline is at: }y=1 \\ \text{Period}=(2\pi)/(2) \\ \text{Period}=\pi \end{gathered}`

With the above characteristics we can now graph the function as;