Given the function f(x) = logg x, construct the function g (x) such that the graph of g (x) is the same as the graph of f(x)

Question

Given the function f(x) = logg x, construct the function g (x) such that the graph of g (x) is the same as the graph of f(x)

but shifted 7 units down, shrunk vertically by a factor of ½, and reflected across the y-axis. In 1-2 sentences, describe the construction of the function and identify the correct function. (2 points)

Answer 1

The function g(x) would be g(x) = -1/2 * log(x) - 7, where the original function f(x) = log(x) is shifted down 7 units, vertically shrunk by a factor of 1/2, and reflected across the y-axis.