Final answer:
The reflected function over the y-axis of F(X) = 5(1/5)^x is F(X) = 5(5)^x.
Step-by-step explanation:
The function given is F(X) = 5(1/5)^x. Reflecting a function over the y-axis essentially replaces every x in the function with -x. Thus, the reflected function of F(X) will have the form F(-X). When we apply this to the original function, we get F(-X) = 5(1/5)^-x. Simplifying the exponent -x as division, we can rewrite (1/5)^-x as 5^x. Hence, the reflected function will be F(X) = 5(5)^x.
When a function is reflected over the y-axis, the x-values change to their opposites, while the y-values remain the same. In the given function F(X) = 5(1/5)^x, reflecting it over the y-axis means changing the sign of the coefficient of x. Therefore, the equation that represents the reflected function is F(X) = -5(1/5)^x (option a).