determine the amplitude and period of each function. then graph one period of the function.\ny = 3 sin…

determine the amplitude and period of each function. then graph one period of the function.\ny = 3 sin $\frac{1}{2}$x\nthe amplitude is \nthe period is \n(type an exact answer in terms of $pi$. use integers or fractions for any numbers in the expression.)\ndetermine the graph of y = 3 sin $\frac{1}{2}$x.

determine the amplitude and period of each function. then graph one period of the function.\ny = 3 sin $\frac{1}{2}$x\nthe amplitude is \nthe period is \n(type an exact answer in terms of $pi$. use integers or fractions for any numbers in the expression.)\ndetermine the graph of y = 3 sin $\frac{1}{2}$x.

Answer

Explanation:

Step1: Recall amplitude formula

For $y = A\sin(Bx)$, amplitude is $|A|$. Here $A = 3$, so amplitude $=|3| = 3$.

Step2: Recall period formula

The period of $y=\sin(Bx)$ is $T=\frac{2\pi}{|B|}$. Here $B=\frac{1}{2}$, so $T=\frac{2\pi}{\left|\frac{1}{2}\right|}=4\pi$.

Step3: Analyze graph characteristics

The function $y = 3\sin\frac{1}{2}x$ has an amplitude of 3 (oscillates between - 3 and 3) and a period of $4\pi$. Starting at the origin $(0,0)$, it will complete one full cycle in the interval $[0,4\pi]$.

Answer:

The amplitude is 3. The period is $4\pi$. (Note: Without seeing all the graph - options clearly, we can't select the correct graph from A and B. But the above amplitude and period values are correct for the function $y = 3\sin\frac{1}{2}x$.)