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The graph of \(y = 3x - 1\) has a slope of \(3\) and a \(y\)-intercept of \(–1\). The graph of \(y = 3x - 1\) has \(y\)-values of \(\pm 1\) at the points \((0, -1)\) and \((\frac{2}{3}, 1)\), so these will also be points on the graph of \(y = \frac{1}{3x - 1}\). The graph of \(y = 3x - 1\) crosses the \(x\)-axis at \((\frac{1}{3}, 0)\), so a vertical asymptote on the graph of \(y = \frac{1}{3x - 1}\) passes through this point. There is also a horizontal asymptote at \(y = 0\).

The graph has \(y\)-values of \(\pm 1\) at \((4, –1)\) and \((8, 1)\), so the graph of \(y = g(x)\) will pass through these points. The graph of \(y = \frac{1}{g(x)}\) appears to have a vertical asymptote at \(x = 6\), so the graph of \(y = g(x)\) crosses the \(x\)-axis at \((6, 0)\).