1. The problem asks to find the function equation for a graph that is a translation of the cube root function $f(x) = \sqrt[3]{x}$.\n\n2. The general form for a horizontal and vertical translation of $f(x)$ is $$g(x) = \sqrt[3]{x - h} + k$$ where $h$ is the horizontal shift and $k$ is the vertical shift.\n\n3. From the graph description, the inflection point (center) is at approximately $(7, 0)$, which means the graph is shifted right by 7 units and down by 0 units.\n\n4. Therefore, the function is $$g(x) = \sqrt[3]{x - 7} + 0 = \sqrt[3]{x - 7}.$$\n\n5. This matches the points given: at $x=6$, $g(6) = \sqrt[3]{6-7} = \sqrt[3]{-1} = -1$, and at $x=8$, $g(8) = \sqrt[3]{8-7} = \sqrt[3]{1} = 1$, confirming the translation.