Question

To transform f(x)=x2+12
to f(x−3)
, which of the following shows the order in which operations should be performed? (1 point)
Responses

Square (x−3)
, subtract 3, and add 12.
Square left parenthesis x minus 3 right parenthesis , subtract 3, and add 12.

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

Square (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, square (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.

The operations to do this are:

1. Substitute \( x - 3 \) in place of \( x \).
2. Square the result.
3. Add 12.

Thus, the correct order of operations for transforming the function is:

**Square \( (x - 3) \), add 12.**

Therefore, the first option ("Square \( (x - 3) \), subtract 3, and add 12.") is incorrect, as we don't subtract 3 after squaring.

The correct option is not listed exactly, but **"Square \( (x - 3) \), add 12."** would entail squaring first, followed by adding 12.

If you are only provided with the options given, the closest in context to your transformation is:

**Square \( (x - 3) \), add 12.**

But since none directly match this, it seems like there might be a small mistake with the provided options. Always ensure to substitute the correct expression before performing further operations.