Answer
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Step 1:: Determine the midline, amplitude, and period of the function.
In this case, $P=\frac{2\pi}{|2|}=\pi$.
The midline of the graph is the horizontal line that passes through the average value of the function. In this case, the average value is the average of the maximum and minimum values, which we will find in the next steps. The amplitude is the distance from the midline to the maximum or minimum points. The period of the graph is the horizontal distance for one complete cycle of the graph.
Step 2:: Find the maximum and minimum points.
The maximum points occur at $x=-\frac{\pi}{2}$ and $x=\frac{\pi}{2}$, and the minimum points occur at $x=0$ and $x=\pi$.
Since the amplitude is 2, the maximum points are at a distance of 2 above the midline, and the minimum points are at a distance of 2 below the midline.
Step 3:: Draw the graph.
d) The minimum points are at $y=3-2=1$ and $x=0$ and $x=\pi$.
Mark these points. Mark these points. e) Draw the graph connecting these points. Double check that this is the graph of the function.
Final Answer
| Maximum: | $(-\frac{\pi}{2}, 5)$, $(\frac{\pi}{2}, 5)$ | | --- | --- | | Minimum: | $(0, 1)$, $(\pi, 1)$ | | Equation of the midline: | $y= 3$ | | Amplitude: | 2 | | Period: | $\pi$ | | Frequency: | $\frac{1}{\pi}$ | | Equation of the graphed function: | $f(x)=- 2\sin(2x)+ 3$ |
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