g(x) is a translation of f(x), we have:
g(x) = f(x) - 3
We have the two functions:
[tex]g(x) = x^2 - 3\\\\f(x) = x^2[/tex]
We can see that g(x) is just a translation of 3 units downwards of f(x), to write g(x) in terms of f(x) we can just replace the first term by f(x):
[tex]g(x) = x^2 - 3 = f(x) - 3[/tex]
So we have:
g(x) = f(x) - 3
If you want to learn more about translations:
https://brainly.com/question/24850937
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