# Question #b237f

You want choice (b) $y = 7 \sin \left(\frac{x}{2}\right)$
The function is often written $y = A \sin \left(k x\right)$ where $A$ is the amplitude, and $k$ determines the frequency at which the function oscillates.
The amplitude is defined as the maximum change in the function from the $y = 0$ position, which occurs when the sin function equals one. For this to happen, the multiplier must be 7. So, in answer to the first part of the question, we can rule out choices (c) and (d), as these have only half the designated amplitude.
The frequency can be trickier. Knowing that the sin function repeats its cycle every time the argument in brackets goes through a multiple of $2 \pi$, we look for the one that will give us the result $2 \pi$ when $x$goes from 0 to $4 \pi$. This will be the one with $\left(\frac{x}{2}\right)$ in the bracket. When $x = 0$, $\left(\frac{x}{2}\right)$ also equals zero. But $x = 4 \pi$ will be the next time that $\left(\frac{x}{2}\right)$ will equal $2 \pi$, and the function will complete one cycle.