Question

To transform f(x)=x2+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.

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

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

Answer 1

To transform the function \( f(x) = x^2 + 12 \) into \( f(x - 3) \), we want to evaluate \( f \) at \( x - 3 \).

We substitute \( x - 3 \) into the function:

\[
f(x - 3) = (x - 3)^2 + 12
\]

Now let's break down the operations needed to achieve this:

1. **Subtract 3 from x**: This gives us \( x - 3 \).
2. **Square the result**: We then square \( (x - 3) \) to get \( (x - 3)^2 \).
3. **Add 12**: Finally, we add 12 to the squared result.

So, the correct order is:

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

Therefore, the option that best describes the order of operations is:

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