The curve above is the graph of a sinusoidal function. It goes through the points $(-12,0)$ and $(2,0)$.
Find the sinusoidal (sine) function that uses the largest STATED $x$-intercept value as it's phase shift and matches the given graph.
If needed, you can enter $\pi=3.1416 \ldots$ as ' $\mathrm{pi}$ ' in your answer, otherwise use at least 3 decimal digits.
\[
f(x)=
\]

Step 1 ：The given points $(-12,0)$ and $(2,0)$ are the x-intercepts of the sinusoidal function. The distance between these two points is $2 - (-12) = 14$ units on the x-axis.

Step 2 ：The period of a sinusoidal function is the distance between two consecutive x-intercepts. Therefore, the period of the given function is $14$ units.

Step 3 ：The standard form of a sine function is $f(x) = A\sin(B(x - C)) + D$, where $A$ is the amplitude, $B$ is the frequency, $C$ is the phase shift, and $D$ is the vertical shift.

Step 4 ：Since the amplitude is not given, we assume it to be $1$. The frequency is the reciprocal of the period, so $B = \frac{1}{14}$.

Step 5 ：The phase shift is the largest stated x-intercept, which is $2$. Therefore, $C = 2$.

Step 6 ：Since the graph passes through the origin, the vertical shift $D = 0$.

Step 7 ：Substituting these values into the standard form, we get $f(x) = \sin\left(\frac{1}{14}(x - 2)\right)$.

Step 8 ：Therefore, the sinusoidal function that uses the largest stated x-intercept value as its phase shift and matches the given graph is $f(x) = \sin\left(\frac{1}{14}(x - 2)\right)$.

Step 9 ：\boxed{f(x) = \sin\left(\frac{1}{14}(x - 2)\right)}