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? (1 point)
Square (x − 3), add 12, and subtract 3 from x.
Subtract 3 from x, square (x − 3), and add 12.
Square (x − 3), subtract 3, and add 12.
Subtract 3 from x, multiply by 2, and add 12.
2 + 12 to f(x − 3), which of the following shows the order in which operations
should be performed? (1 point)
Square (x − 3), add 12, and subtract 3 from x.
Subtract 3 from x, square (x − 3), and add 12.
Square (x − 3), subtract 3, and add 12.
Subtract 3 from x, multiply by 2, and add 12.
Answers
GPT-4o mini
To transform \( f(x) = x^2 + 12 \) to \( f(x - 3) \), you need to evaluate it at \( x - 3 \). This involves the following steps:
1. Substitute \( x - 3 \) into the function, meaning you will replace \( x \) with \( x - 3 \).
2. This results in:
\[
f(x - 3) = (x - 3)^2 + 12
\]
3. Now, you first need to square \( (x - 3) \), then you add 12.
So, the correct order of operations is:
- **Square (x − 3)**
- **Add 12**
Thus, the correct answer is:
- **Square (x − 3), add 12, and subtract 3 from x.** (Although the last part is not necessary for the operation, the first two steps are correct.)
However, if you're looking strictly for the order of operations relevant to the transformation (without mentioning subtracting 3 from x at the end), then just focusing on those two parts is sufficient. But among the options provided, the one that matches closest with the necessary steps is the first option, acknowledging that the "subtract 3 from x" is just indicating the transformation where \( f \) is evaluated.
1. Substitute \( x - 3 \) into the function, meaning you will replace \( x \) with \( x - 3 \).
2. This results in:
\[
f(x - 3) = (x - 3)^2 + 12
\]
3. Now, you first need to square \( (x - 3) \), then you add 12.
So, the correct order of operations is:
- **Square (x − 3)**
- **Add 12**
Thus, the correct answer is:
- **Square (x − 3), add 12, and subtract 3 from x.** (Although the last part is not necessary for the operation, the first two steps are correct.)
However, if you're looking strictly for the order of operations relevant to the transformation (without mentioning subtracting 3 from x at the end), then just focusing on those two parts is sufficient. But among the options provided, the one that matches closest with the necessary steps is the first option, acknowledging that the "subtract 3 from x" is just indicating the transformation where \( f \) is evaluated.