To transform f(x)=x2+12

Question

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

Square (x−3)
(
𝑥
−
3
)
, subtract 3, and add 12.
Square left parenthesis x minus 3 right parenthesis , subtract 3, 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, multiply by 2, and add 12.
Subtract 3 from x, multiply by 2, and add 12.

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

Answer 1

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

Here's how the process works step by step:

1. Start with the expression \( x - 3 \).
2. Square it: \( (x - 3)^2 \).
3. Then add 12.

So the correct sequence of operations is:

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

Based on the responses provided, it seems that the phrasing needs clarification, but the answer aligns with "Square (x−3), add 12".

None of the provided options perfectly match this sequence. However, if the options meant to say that squaring comes before adding 12, then the closest match would be:

"Square \( (x - 3) \), add 12, and subtract 3 from x."

Although the phrase "subtract 3 from x" doesn't directly describe the transformation process, it acknowledges that you're working with \( x - 3 \) at the start.

Thus, the best option that aligns with our understanding would be the first or second one identifying the square and addition. If you have to select one explicitly, choose one mentioning the squaring of \( (x-3) \) first.