To describe how the graph of each function can be obtained from the graph of f, we need to understand the effect of the given transformations.
1. Y = f(3x):
- The function f(3x) means that we are compressing the graph horizontally by a factor of 3.
- To obtain the new graph, start with the original graph of f, and for each point (x, y) on the graph:
- Multiply the x-coordinate by 1/3 to compress it horizontally.
- The y-coordinate remains the same.
- This transformation causes the graph to be narrower, as it is squeezed towards the y-axis.
2. Y = f(1/3x):
- The function f(1/3x) means that we are stretching the graph horizontally by a factor of 3.
- To obtain the new graph, start with the original graph of f, and for each point (x, y) on the graph:
- Multiply the x-coordinate by 3 to stretch it horizontally.
- The y-coordinate remains the same.
- This transformation causes the graph to be wider, as it is expanded away from the y-axis.
In summary, for Y = f(3x), the graph is compressed horizontally by a factor of 3, while for Y = f(1/3x), the graph is stretched horizontally by a factor of 3.