Question

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}`?

Answer 1

[AI-generated answer — Bot GPT 3.5]

To translate the graph of `f(x) = x^2` to the right 7 units, we need to replace `x` with `(x - 7)` in the function rule. This will shift the graph horizontally to the right.

So, the new function rule for `g(x)` is:

`g(x) = (x - 7)^2`

To further translate the graph of `g(x)` up 2 units, we add 2 to the function rule:

`g(x) = (x - 7)^2 + 2`

Therefore, the function rule for `g(x)` is `(x - 7)^2 + 2`.