describe the transformation done by y=1/x to get y = 1/4x -12
vertical shrink by 4
shift down 12
To describe the transformation from y = 1/x to y = 1/4x - 12, we can analyze how each modification in the equation affects the graph.
1. Scaling: The coefficient 1/4 in front of the x indicates a horizontal scaling by a factor of 4. This means the graph becomes narrower, as if it is being squeezed towards the y-axis.
2. Shifting: The constant term -12 indicates a vertical shift downwards by 12 units. This means the entire graph is shifted downward, making all points vertically lower.
By combining these transformations, we can say that the original graph of y = 1/x is being squeezed towards the y-axis by a factor of 4 and shifted downward by 12 units to form y = 1/4x - 12.