Question

The maximum value of the function y = 2 - |x - 3| is :

• A. 0
• B. 3
• C. 2
• D. 5

Answer 1

The Correct Option is C

To find the maximum value of the function \( y = 2 - |x - 3| \), we need to analyze the expression involving the absolute value.

The function \( y = 2 - |x - 3| \) can be interpreted as a transformation of the absolute value function \( y = |x| \), which has its vertex shifted to the point where \( |x - 3| \) is zero.

Step 1: Determine the point where the expression inside the absolute value becomes zero. This happens when \( x - 3 = 0 \) or \( x = 3 \).

Step 2: Substitute \( x = 3 \) into the function to find the value of \( y \) at this point:

\( y = 2 - |x - 3| = 2 - |3 - 3| = 2 - 0 = 2 \)

Step 3: Analyze the function behavior for values of \( x \) around \( 3 \):

• For \( x < 3 \), the expression \( |x - 3| \) increases, causing \( y \) to decrease.
• For \( x > 3 \), the same increasing pattern occurs, keeping \( y \) on the decline.

Thus, the highest point or maximum value of the function is at \( x = 3 \), giving \( y = 2 \).

Therefore, the maximum value of the function is \( 2 \).