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

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

So, let's go through the transformation step-by-step:

1. Start with the original function: \[ f(x) = x^2 + 12 \]

2. Now, we substitute \( x-3 \) for \( x \): \[ f(x-3) = (x-3)^2 + 12 \]

3. To evaluate \((x-3)^2\), we perform the following operations:

   • Subtract 3 from \( x \)
   • Square the result
   • Then, add 12 to the squared result

Now, let's check which option correctly describes this order:

1. Subtract 3 from x, multiply by 2, and add 12 - Incorrect
2. Subtract 3 from x, square (x-3), and add 12 - Correct
3. Square (x-3), add 12, and subtract 3 from x - Incorrect
4. Square (x-3), subtract 3 and add 12 - Incorrect

The correct option is: Subtract 3 from x, square (x-3), and add 12.