How would you describe the difference between the graphs of f(x) = x^2 +4 and
g(y) - y^2 +4?

Step-by-step explanation:

The function is a positive upwards opening parabola with the vertex at (0, 4), whereas

the function is a positive rightwards opening parabola (sideways parabola) with the vertex at (4, 0). This means that answer to this is that g(y) is reflected over the x axis whereas f(x) is reflected over the y axis.