The maximum value of the function y = 2 − |x − 3| is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 2
An absolute value is never negative:
\(|x - 3| \ge 0\)
\(y = 2 - |x - 3| \le 2\)
The value 2 is reached when |x − 3| = 0, that is, at x = 3:
\(y(3) = 2 - 0 = 2\)
So the maximum value is 2 (at x = 3).