The graph of f(x)=1/x^2 is horizontally compressed by a factor of 14, then shifted to the right 9 units and up 3 units.
g(x) = 1/(14(x-9))^2 + 3
To horizontally compress the graph of f(x)=1/x^2 by a factor of 14, we need to replace x with 1/14x.
Then, to shift the graph to the right 9 units, we add 9 to the x-values:
g(x) = 1/(1/14x + 9)
Next, to shift the graph up 3 units, we add 3 to the y-values:
h(x) = 1/(1/14x + 9) + 3
So, the transformed function is h(x) = 1/(1/14x + 9) + 3.
To horizontally compress the graph of the function f(x) = 1/x^2 by a factor of 14, you need to multiply the x-values by 1/14. This will make the graph narrower.
To shift the compressed graph 9 units to the right, you need to subtract 9 from the x-values. This will move the graph horizontally.
To shift the graph up 3 units, you need to add 3 to the y-values. This will move the graph vertically.
Therefore, the transformed function g(x) can be written as:
g(x) = 1/( (1/14)*(x-9) )^2 + 3
This represents the desired transformations of horizontally compressing the graph by a factor of 14, shifting it 9 units to the right, and moving it up by 3 units.