1. The problem states that the graph of $y=\frac{1}{x}$ is transformed to the graph of $y=5(x-3)-4$ and asks for the scale factor of the vertical stretch about the x-axis. 2. First, note the original function: $$y=\frac{1}{x}$$ 3. The transformed function given is: $$y=5(x-3)-4$$ 4. However, this transformed function is linear, not a transformation of $y=\frac{1}{x}$. It seems there might be a misunderstanding or typo in the problem statement. 5. Assuming the intended transformation is from $y=\frac{1}{x}$ to $y=5\cdot\frac{1}{x-3}-4$, which is a vertical stretch by a factor of 5, a horizontal shift right by 3, and a vertical shift down by 4. 6. The vertical stretch about the x-axis is represented by the coefficient multiplying the function, which is 5. 7. Therefore, the scale factor of the vertical stretch is $5.0$ (to the nearest tenth). Final answer: $5.0$