1. The problem asks us to determine which ordered pairs lie on the graph of the exponential function $$f(x) = 3 \left(\frac{1}{4}\right)^x$$. 2. To check if a point $ (a, b) $ lies on the graph, we substitute $ x = a $ into the function and see if the output equals $ b $. 3. The function is $$f(x) = 3 \left(\frac{1}{4}\right)^x$$. 4. Check each point: - For $ (0, 3) $: $$f(0) = 3 \left(\frac{1}{4}\right)^0 = 3 \times 1 = 3$$ Since $f(0) = 3$, the point $ (0, 3) $ lies on the graph. - For $ (2, \frac{3}{16}) $: $$f(2) = 3 \left(\frac{1}{4}\right)^2 = 3 \times \frac{1}{16} = \frac{3}{16}$$ Since $f(2) = \frac{3}{16}$, the point $ (2, \frac{3}{16}) $ lies on the graph. - For $ (12, 0) $: $$f(12) = 3 \left(\frac{1}{4}\right)^{12} = 3 \times \frac{1}{4^{12}} > 0$$ Since $f(12)$ is positive and not zero, the point $ (12, 0) $ does not lie on the graph. - For $ (-2, 48) $: $$f(-2) = 3 \left(\frac{1}{4}\right)^{-2} = 3 \times 4^2 = 3 \times 16 = 48$$ Since $f(-2) = 48$, the point $ (-2, 48) $ lies on the graph. 5. Final answer: The points $ (0, 3) $, $ (2, \frac{3}{16}) $, and $ (-2, 48) $ lie on the graph of the function.