Suppose the graph of f is given describe how the graph of each function can be obtained from the graph of f?
Y=f(3x)
Y=f(1/3x)
To obtain the graph of the function y = f(3x), you would compress the graph of f horizontally by a factor of 3. This means that each point on the graph of f would now be located at 1/3 of its original horizontal distance. This would make the graph narrower and more compact.
To obtain the graph of the function y = f(1/3x), you would stretch the graph of f horizontally by a factor of 3. This means that each point on the graph of f would now be located at 3 times its original horizontal distance. This would make the graph wider and more spread out.
To describe how the graph of each function can be obtained from the graph of f, we need to understand the transformations that occur when manipulating the input variable (x) inside the function.
1. Y = f(3x):
- The 3 in front of the x indicates a horizontal compression of the graph by a factor of 1/3. This means that the graph will be compressed horizontally by shrinking the x-values.
- To obtain the graph of Y = f(3x) from the graph of f, you need to take each x-value on the original graph and divide it by 3. The corresponding y-values remain the same.
2. Y = f(1/3x):
- The 1/3 in front of the x indicates a horizontal stretch of the graph by a factor of 3. This means that the graph will be stretched horizontally by enlarging the x-values.
- To obtain the graph of Y = f(1/3x) from the graph of f, you need to take each x-value on the original graph and multiply it by 3. The corresponding y-values remain the same.
In summary:
- For Y = f(3x), divide each x-value on the original graph of f by 3.
- For Y = f(1/3x), multiply each x-value on the original graph of f by 3.
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.