Sketch the graph of \(y = |2x + 1|\)
Solution
The function \(y = |2x + 1|\) is an absolute value function, which creates a V-shaped graph.
1. The expression inside the absolute value, \(2x + 1\), equals zero at \(x = -\frac{1}{2}\). This is the x-coordinate of the vertex.
2. The vertex of the graph is at \((-\frac{1}{2}, 0)\).
3. When \(x = 0\), \(y = |2(0) + 1| = 1\). This gives the y-intercept at \((0, 1)\).
4. For \(x > -\frac{1}{2}\), the graph follows \(y = 2x + 1\).
5. For \(x < -\frac{1}{2}\), the graph follows \(y = -(2x + 1) = -2x - 1\).
The graph is symmetric about the vertical line \(x = -\frac{1}{2}\).
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