To transform f(x)=x^2+12 to f(x−3), which of the following shows the order in which operations should be performed?

Question

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

Subtract 3 from x, multiply by 2, and add 12.

Square (x−3), subtract 3, and add 12.

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

Answer 1

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

Here's how to do it step-by-step:

1. Take \( x - 3 \) (subtract 3 from \( x \)).
2. Square the result, which means you calculate \( (x - 3)^2 \).
3. Finally, add 12.

So, the correct order of operations is:

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

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