how would you describe the difference between the graphs of f(x)=x^2 + 4 and g(y)=y^2+4?
a. g(y) is a reflection of f(x) over the line y=x.
b. g(y) is a reflection of f(x) over the x-axis.
c. g(y) is a reflection of f(x) over the y-axis.
d. g(y) is a reflection of f(x) over the line y=1.

Option: A is the correct answer.

       A.   g(y) is a reflection of f(x) over the line y=x.

We know that the reflection of a parent function f(x) about the line y=x is such that the x and the y-values change places i.e. there is a swap in the x and y variables.

        Here we are given a parent function f(x) as:

Also, the function g(y) is given by:

Clearly we could see that the x and the y-variables are swapped.

Hence, the transformation g(y) is a reflection of f(x) over the line y=x.