Given the functions f(x)=1x−2+1 and g(x)=1x+5+9 .

Which statement describes the transformation of the graph of function f onto the graph of function g?

The graph shifts 8 units right and 7 units down
The graph shifts 7 units left and 8 units up.
The graph shifts 7 units right and 8 units down.
The graph shifts 8 units left and 7 units up.

f(x) = (x-2)+1

g(x) = (x+5)+9 = ((x-2)+7)+(1+8)
so, B

To determine the transformation between the graphs of the functions f(x) and g(x), we need to compare the changes in the equations.

The function f(x) = 1/x - 2 + 1 can be simplified as f(x) = 1/x - 1.

The function g(x) = 1/x + 5 + 9 can be simplified as g(x) = 1/x + 14.

Comparing the two functions, we can observe the following changes:
1. The constant term in function f(x) is -1, while in function g(x) it is 14. This indicates a vertical shift upward of 15 units (14 - (-1) = 15).
2. The coefficient of x in both functions is 1, meaning there is no horizontal stretch or compression.
3. There is no change in the reciprocal since the coefficient remains the same.

Based on these comparisons, we can conclude that the graph of function f(x) shifts 7 units right (no change in coefficient) and 15 units up (change in constant term) to transform into the graph of function g(x).

Therefore, the correct statement describing the transformation is: "The graph shifts 7 units right and 15 units up."

The correct statement is: The graph shifts 7 units left and 8 units up.