Question

to transform f9x)=x^2+12 to f(x-3), which of the following shows the order in which operations should be performed?
a square (x-3), subtract 3, and add 12
b square (x-3), add 12, and subtract 3 from x
c subtract 3 from x, multiply by 2, and add 12
d 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 is the step-by-step process for how to do this:

1. **Subtract 3 from x**: Since we are replacing \( x \) with \( x - 3 \), the first operation is \( x - 3 \).

2. **Square (x-3)**: Next, we take the result from the first step and square it: \( (x - 3)^2 \).

3. **Add 12**: Finally, we add 12 to complete the transformation: \( (x - 3)^2 + 12 \).

So the correct order of operations is to first "subtract 3 from x", then "square (x-3)", and finally "add 12".

The correct answer is:

**d) subtract 3 from x, square (x-3), and add 12**.