How is the the graph of y=1/2x-6
obtained from the graph of y=1/x
?
A) Vertically stretched by a factor of 2 and shifted right by 3 units.
B) Vertically stretched by a factor of 3 and shifted right by 2 units.
C) Horizontally stretched by a factor of 2 and shifted left by 3 units. <my answer
D) Horizontally compressed by a factor of 2 and shifted right by 3 units.
1/(2x-6) = 1/2 * 1/(x-3)
so, shifted right 3 and vertically shrunk by 2.
Hmmm. Not a choice. So, equivalently,
1/(2x-6) = 1/(2(x-3))
shifted by 3, horizontally shrunk by 2.
(D)
http://www.wolframalpha.com/input/?i=plot+y%3D1%2Fx,+y%3D1%2F(2x-6)
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.