question #20 write a function f(x) to match the dotted graph. use the form f(x)=a sin(bx) f(x)= graph and…

question #20 write a function f(x) to match the dotted graph. use the form f(x)=a sin(bx) f(x)= graph and submit hint: click the graph to see the exact points.

question #20 write a function f(x) to match the dotted graph. use the form f(x)=a sin(bx) f(x)= graph and submit hint: click the graph to see the exact points.

Answer

Explanation:

Step1: Determine the amplitude $a$

The amplitude is half the vertical distance between the maximum and minimum values. The maximum value is 4 and the minimum is - 4. So, $a=\frac{4 - (-4)}{2}=4$.

Step2: Determine the period $T$

The period is the horizontal distance between two consecutive maximum - points. From the graph, two consecutive maximum - points are at $x = 600$ and $x = 1000$, so $T=1000 - 600 = 400$.

Step3: Calculate the value of $b$

The formula for the period of $y = a\sin(bx)$ is $T=\frac{2\pi}{b}$. Rearranging for $b$, we get $b=\frac{2\pi}{T}$. Substituting $T = 400$, we have $b=\frac{2\pi}{400}=\frac{\pi}{200}$.

Answer:

$f(x)=4\sin\left(\frac{\pi}{200}x\right)$