Question

To transform f(x)=x^2 +12 to f(x−3) , which of the following shows the order in which operations should be performed? (1 point) Responses Subtract 3 from x, multiply by 2, and add 12. Subtract 3 from x, multiply by 2, and add 12. Square (x−3) , subtract 3, and add 12. Square left parenthesis x minus 3 right parenthesis , subtract 3, and add 12. Subtract 3 from x, square (x−3) , and add 12. Subtract 3 from x, square left parenthesis x minus 3 right parenthesis , and add 12. Square (x−3) , add 12, and subtract 3 from x.

Answer 1

To transform the function \( f(x) = x^2 + 12 \) to \( f(x - 3) \), you need to replace \( x \) with \( (x - 3) \) in the original function.

Here are the steps involved:

1. **Subtract 3 from \( x \)**: This step is implicit since you're replacing \( x \) with \( (x - 3) \).
2. **Square \( (x - 3) \)**: You then square this expression.
3. **Add 12**: Finally, you add 12 to the squared result.

So, the operations should be performed in the following order:

- Subtract 3 from \( x \)
- Square \( (x - 3) \)
- Add 12

Thus, the correct response is:

**Subtract 3 from x, square (x−3), and add 12.**