If the graph of f(x) is vertically compressed by a factor of 1/3 to get the graph of g(x), this means that every y-coordinate of the graph of f(x) is multiplied by 1/3 to get the corresponding y-coordinate of the graph of g(x). To find the function rule for g(x), we can start with the function rule for f(x) and apply the vertical compression.
The function rule for f(x) is f(x) = 3x^2 + 12.
To vertically compress the graph of f(x) by a factor of 1/3, we can divide the entire function by 1/3, which is the same as multiplying by 3. This gives:
g(x) = 3/3 * (3x^2 + 12) = (3/3) * 3x^2 + (3/3) * 12 = x^2 + 4
Therefore, the simplified function rule for function g is g(x) = x^2 + 4.