1. **Problem statement:** Reflect the function $f(x) = \frac{1}{10} \cdot 10^x$ across the y-axis. 2. **Reflection rule:** Reflecting a function across the y-axis means replacing $x$ by $-x$ in the function. So the reflected function is $g(x) = f(-x)$. 3. **Apply the rule:** $$g(x) = \frac{1}{10} \cdot 10^{-x}$$ 4. **Simplify the expression:** $$g(x) = \frac{1}{10} \cdot \frac{1}{10^x} = \frac{1}{10^{x+1}}$$ 5. **Interpretation:** The reflected function $g(x)$ decreases as $x$ increases, which matches the description of the curve dropping steeply from left to right. **Final answer:** $$g(x) = \frac{1}{10^{x+1}}$$