Final answer:
Transformations of 1/x include reflection across the y-axis, vertical compression, horizontal shift, and vertical reflection, each with distinct effects on the graph. Without additional context, we cannot associate any single transformation as the correct description for altering 1/x.
Step-by-step explanation:
To describe transformations of the function 1/x, we need to understand how different modifications affect its graph. Here are the basic transformations and their effects:
- A reflection across the y-axis would mean that for every point (x, y) on the graph of 1/x, there is a corresponding point (-x, y), mirroring the graph over the y-axis. However, since the graph of 1/x is symmetrical with respect to the origin, this transformation does not change its appearance.
- A vertical compression would result in multiplying the output of the function by a factor between 0 and 1, thus squeezing the graph towards the x-axis without altering the x-coordinates of the points on the graph.
- A horizontal shift involves adding or subtracting a constant value to the x-coordinate of every point on the graph, which moves the entire graph to the right or left.
- A vertical reflection would invert the graph over the x-axis, turning every point (x, y) into (x, -y).
For the basic function 1/x, none of the options A) Reflection across the y-axis, B) Vertical compression, C) Horizontal shift, or D) Vertical reflection can be uniquely associated with a transformation without additional context. Each of these transformations alters the graph differently.