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9709 P33 - Nov 2021 - Q2
1492
Sketch the graph of \(y = |2x - 3|\).
Solution
The function \(y = |2x - 3|\) is an absolute value function, which creates a V-shaped graph.
1. The expression inside the absolute value, \(2x - 3\), is zero when \(x = \frac{3}{2}\). This is the vertex of the V-shape.
2. For \(x < \frac{3}{2}\), \(2x - 3\) is negative, so \(y = -(2x - 3) = -2x + 3\).
3. For \(x > \frac{3}{2}\), \(2x - 3\) is positive, so \(y = 2x - 3\).
4. The graph consists of two linear pieces: \(y = -2x + 3\) for \(x < \frac{3}{2}\) and \(y = 2x - 3\) for \(x > \frac{3}{2}\), meeting at the vertex \((\frac{3}{2}, 0)\).
