Question

To transform f(x)=x2+12
f
(
x
)
=
x
2
+
12
to f(x−3)
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)
(
x
−
3
)
, add 12, and subtract 3 from x.
Square left parenthesis x minus 3 right parenthesis , add 12, and subtract 3 from x.

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

Square (x−3)
(
x
−
3
)
, subtract 3, and add 12.

Answer 1

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

Here are the steps involved:

1. **Subtract 3 from x**: This gives you \( x-3 \).
2. **Square \( (x-3) \)**: You compute \( (x-3)^2 \).
3. **Add 12**: Finally, you add 12 to the result from the previous step.

Putting this together, the order of operations is:

1. Subtract 3 from \( x \).
2. Square the result, \( (x-3) \).
3. Add 12.

Thus, the correct response is:

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