The function \(f(x) = x^2\) was transformed to create the function \(g(x) = f(x-2) + 5\).
When a function is transformed, the operations done to the function affect its graph. In this case, the transformation is a combination of translating the graph of function \(f\) and shifting it vertically.
1. The function is translated 2 units to the right because of the \(x-2\) inside the function. This means that every point on the graph of function \(f\) is moved horizontally 2 units to the right to create the graph of function \(g\).
2. The function is shifted 5 units up because of the \(+5\) outside the function. This means that every point on the graph of function \(f\) is shifted vertically 5 units up to create the graph of function \(g\).
Therefore, the correct answer to complete the sentence is: "The graph of \(f\) is translated 2 units to the right and 5 units up to create the graph of function \(g\)."
