A function is defined as f(x) = |x - 3| + |x + 2|. What is the minimum value of f(x)?
Correct: E
The function f(x) = |x - 3| + |x + 2| represents the sum of the distances from x to 3 and from x to -2. The minimum value occurs when x is between -2 and 3, inclusive. In this case, the sum of the distances is the distance between -2 and 3, which is 3 - (-2) = 5. To see this, consider x = -2, then f(-2) = |-2 - 3| + |-2 + 2| = |-5| + 0 = 5. Consider x = 3, then f(3) = |3 - 3| + |3 + 2| = 0 + |5| = 5. Any value between -2 and 3 will result in a total of 5.