The graph of `g(x)` is `f(x)` translated to the right 7 units and up 2 units. What is the function rule for `g(x)` given `f(x)=x^{2}`?
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To translate the graph of f(x) to the right 7 units, we replace x with (x - 7) in the function rule. So, the expression for g(x) becomes f(x - 7).
To translate the graph of f(x) up 2 units, we add 2 to the expression for g(x). Therefore, the function rule for g(x) is g(x) = f(x - 7) + 2.
Substituting f(x) = x^2, we have g(x) = (x - 7)^2 + 2.
Thus, the function rule for g(x) is g(x) = (x - 7)^2 + 2.