To create a sine function that reflects the specified transformations, we start with the basic sine function, which is given by:
\[ f(x) = \sin(x) \]
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Horizontal compression by a factor of 3: This transformation affects the period of the sine function. The period of the sine function \(\sin(x)\) is \(2\pi\). With a horizontal compression by a factor of 3, the new period becomes:
\[ \text{New Period} = \frac{2\pi}{3} \]
To achieve this effect, we replace \(x\) with \(3x\) in the function:
\[ g(x) = \sin(3x) \]
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Reflection across the x-axis: Reflecting across the x-axis means negating the function. This is achieved by multiplying the entire sine function by -1:
\[ h(x) = -\sin(3x) \]
Putting it all together, the equation for the sine function that has a horizontal compression by a factor of 3 and a reflection across the x-axis is:
\[ h(x) = -\sin(3x) \]
Thus, the final answer is:
\[ \boxed{-\sin(3x)} \]