Question

To transform f (x) = x^2 + 12 to f (x - 3), what steps would you take and what would the final answer be?

Answer 1

Step 1: Replace x by x−3 in f(x): f(x−3) = (x−3)^2 + 12.
Step 2: Expand the square: (x−3)^2 = x^2 − 6x + 9.
Step 3: Add 12 and simplify: x^2 − 6x + 9 + 12 = x^2 − 6x + 21.

So f(x−3) = x^2 − 6x + 21.