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, square (x−3)
, and add 12.
Subtract 3 from x, square left parenthesis x minus 3 right parenthesis , and add 12.

Subtract 3 from x, multiply by 2, and add 12.
Subtract 3 from x, multiply by 2, and add 12.

Square (x−3)
, add 12, and subtract 3 from x.
Square left parenthesis x minus 3 right parenthesis , add 12, and subtract 3 from x.

Square (x−3)
, subtract 3, and add 12.
Square left parenthesis x minus 3 right parenthesis , subtract 3, and add 12.

Answer 1

To transform \( f(x) = x^2 + 12 \) into \( f(x-3) \), you replace \( x \) with \( x-3 \) in the function. This means the following steps are involved:

1. **Subtract 3 from x**: This gives you \( x - 3 \).
2. **Square (x - 3)**: You take the result from the first step and square it; this results in \( (x - 3)^2 \).
3. **Add 12**: Finally, you add 12 to the result of the squaring.

So, the correct order of operations is:

1. Subtract 3 from x.
2. Square (x - 3).
3. Add 12.

Therefore, the correct response is:
**Subtract 3 from x, square (x - 3), and add 12.**