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

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, 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.

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

Answer 1

To transform the function \( f(x) = x^2 + 12 \) to \( f(x - 3) \), you need to substitute \( x - 3 \) into the original function. Here's the step-by-step process:

1. Substitute \( x - 3 \) in place of \( x \) in the function \( f(x) \):
\[
f(x - 3) = (x - 3)^2 + 12
\]

2. The operations performed are:
- Subtract 3 from \( x \) (which gives us \( x - 3 \))
- Square the result \( (x - 3)^2 \)
- Add 12.

Based on this process, the correct sequence of operations is:
- Subtract 3 from \( x \)
- Square \( (x - 3) \)
- Add 12.

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