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, 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.

Answer 1

To transform the function \( f(x) = x^2 + 12 \) to \( f(x-3) \), you need to follow these steps:

1. Substitute \( x-3 \) in place of \( x \) in the original function.
2. This gives us \( f(x-3) = (x-3)^2 + 12 \).

Now, identifying the operations in correct order:

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

So the correct sequence of operations is:

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

Therefore, the correct response is:

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