To transform f(x)=x2+12

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.

GPT-4o mini · Answer

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.