Question

The maximum value of \( y = 12 - |x - 12| \) in the range \( -11 \leq x \leq 11 \) is:

• A. 12
• B. 11
• C. 10
• D. 9
• E. 35

Hint:

The absolute value function \( |x - c| \) achieves its minimum value of 0 when \( x = c \), so substitute this value into the equation to find the maximum or minimum value of \( y \).

Answer 1

The Correct Option is B

The given expression is \( y = 12 - |x - 12| \). The absolute value function \( |x - 12| \) is minimized when \( x = 12 \), since the absolute value of a number is always non-negative, and the minimum occurs when the number inside the absolute value is zero. 
Thus, for \( x = 12 \): \[ y = 12 - |12 - 12| = 12 - 0 = 12 \] For values of \( x \) within the given range \( -11 \leq x \leq 11 \), \( |x - 12| \) increases, leading to smaller values of \( y \). 
Therefore, the maximum value of \( y \) in the given range is \( \boxed{11} \), which occurs when \( x = 12 \).