Discussion
Choose the correct expression for \(f(x)\) given in the graph.
Answer: C
The graph is \(f(x) = 2 - |x - 1|\).
The graph is an inverted V with its peak at (1, 2) and slopes of +1 and -1. A function \(c - |x - h|\) has exactly that shape, with its peak at \((h, c)\), so \(h = 1\) and \(c = 2\).
Check points: \(f(0) = 2 - 1 = 1\), \(f(3) = 2 - 2 = 0\) and \(f(-3) = 2 - 4 = -2\), all on the graph.
\(1 - |x - 1|\) has the right shape but peaks at 1. The two expressions with \(+|x - 1|\) form an upright V, with a minimum, not a maximum, at \(x = 1\).
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