Choose the correct expression for \(f(x)\) given in the graph.

Key features: the graph is a V-shaped (absolute value) curve with a peak at (1, 2) and straight lines of slope ±1 on either side.

• Vertex (peak) at x = 1 with value 2, so the formula should use |x − 1| and be centered at 1 with a constant term 2.

• The graph is upside down (a maximum at the vertex), so the absolute value is subtracted from 2 rather than added.

• Slopes on the sides are ±1, so the coefficient in front of |x − 1| is 1.

Putting these together gives: f(x) = 2 − |x − 1|

Quick checks:

1. At x = 1: f(1) = 2 − |1 − 1| = 2, matching the peak.

2. At x = 3: f(3) = 2 − |3 − 1| = 0, matching the plotted point near (3, 0).

3. At x = −3: f(−3) = 2 − |−3 − 1| = −2, consistent with the left-side value shown.