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
Subtract 3 from x, multiply by 2, and add 12
Subtract 3 from x, square (x-3), and add 12
Square (x-3), 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 \( f(x-3) \), 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.**