To determine how the graph of y = 1/2x - 6 is obtained from the graph of y = 1/x, we need to understand the transformations that have been applied.
The original equation y = 1/x represents a hyperbola. It has a vertical asymptote at x = 0 and a horizontal asymptote at y = 0. The graph passes through the points (1, 1), (-1, -1), (-2, -0.5), (2, 0.5), and so on.
The given equation y = 1/2x - 6 is similar to the original equation y = 1/x, but with some modifications.
Let's analyze the given equation y = 1/2x - 6:
1. Horizontal Stretch: The coefficient in front of x determines the horizontal stretch or compression factor. In this case, as there is a coefficient of 1/2 in front of x, it indicates a horizontal stretch. So, the graph has been stretched horizontally by a factor of 2.
2. Horizontal Shift: The constant term (-6) indicates a horizontal shift. However, we need to be careful with the sign. Since it is -6, it means a shift to the right by 6 units, not a shift to the left.
Based on the transformations mentioned above, it can be concluded that the graph of y = 1/2x - 6 is obtained by horizontally stretching the graph of y = 1/x by a factor of 2 and shifting it right by 6 units.
Therefore, none of the provided options match the correct transformation.