Question

Find the minimum of the function \[ f(x) = |x+2| \]

• A. \( x = -2 \)
• B. \( x = 0 \)
• C. \( x = 2 \)
• D. \( x = -4 \)

Hint:

The minimum of an absolute value function occurs where the expression inside the absolute value is equal to zero.

Answer 1

The Correct Option is A

We are asked to find the minimum of the function \( f(x) = |x+2| \). ### Step 1: Understand the Absolute Value Function The function \( f(x) = |x + 2| \) represents the distance between \( x \) and \( -2 \) on the real number line. The minimum value of the absolute value function occurs when the expression inside the absolute value is zero. ### Step 2: Set the Inside of the Absolute Value Equal to Zero To minimize \( f(x) \), we set \( x + 2 = 0 \): \[ x = -2 \] Thus, the minimum occurs at \( x = -2 \). The minimum value of the function is: \[ f(-2) = |(-2) + 2| = 0 \] Thus, the correct answer is: \[ \boxed{(A) x = -2} \]