to transform f(x) = x^2 + 12 to f (x - 3), which of the following shows the order in which operations should be performed

Question

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 \( f(x) = x^2 + 12 \) into \( f(x - 3) \), you need to replace \( x \) with \( (x - 3) \) in the original function.

Starting with \( f(x) = x^2 + 12 \), we replace \( x \) with \( (x - 3) \):

1. Substitute \( (x - 3) \) into the function: \( f(x - 3) = (x - 3)^2 + 12 \).

Now, let's analyze the order of operations involved in this transformation:

• First, you need to subtract 3 from \( x \): \( (x - 3) \).
• Next, you square the result: \( (x - 3)^2 \).
• Finally, you add 12 to that squared result.

Looking at the answer choices provided:

• a. square (x - 3), subtract 3, and add 12. (Incorrect order)
• b. square (x - 3). add 12, and subtract 3 from x. (Incorrect order)
• c. subtract 3 from x, multiply by 2, and add 12. (Not relevant to required transformation)
• d. subtract 3 from x, square (x - 3), and add 12. (Correct order)

The correct choice is d. subtract 3 from x, square (x - 3), and add 12.