1. The problem asks for the new location of the point $(2, \frac{9}{16})$ on the function $f(x) = \left(\frac{3}{4}\right)^x$ after reflecting the function across the x-axis. 2. Reflection across the x-axis changes the output values by multiplying them by $-1$. The formula for the reflected function is: $$f_{reflected}(x) = -f(x)$$ 3. Given the point $(2, \frac{9}{16})$ lies on $f(x)$, the reflected point will be: $$\left(2, -\frac{9}{16}\right)$$ 4. Therefore, the new location of the point after reflection is $(2, -\frac{9}{16})$.