The function f(x) = 5^x + 2 is an exponential function with a base of 5 and a vertical shift of 2 units upwards. The function g(x) = 5^(-x) + 6 is also an exponential function with a base of 5, but it has a vertical shift of 6 units upwards and a reflection across the y-axis.
Compared to the parent function f(x), the transformed function g(x) is shifted 4 units upwards and has a reflection across the y-axis. This means that the graph of g(x) is a mirror image of the graph of f(x) with respect to the y-axis and is shifted upwards by 4 units.
The transformation of g(x) reflects the original function f(x) across the y-axis and moves it up by 4 units. This change results in a different shape for the graph of g(x) compared to f(x).