Piecewise Linear Function Sketching

00:00 3 marks

Sketch the graph of a piecewise-defined function where the function is defined differently on two intervals. For example, let \(f(x) = \begin{cases} 2x+1 & \text{for } x < 0 \\ -x+3 & \text{for } x \geq 0 \end{cases}\). Ensure that you clearly mark the boundary point at \(x=0\) and indicate whether the corresponding endpoint is included or excluded.

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Hint

Plot each segment separately and carefully note the boundary at \(x = 0\).

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Complete Answer

The graph should consist of two straight-line segments: one for \(x < 0\) defined by \(y = 2x+1\) and one for \(x \geq 0\) defined by \(y = -x+3\). The boundary at \(x=0\) must be clearly marked, with an open circle at \((0, 1)\) and a closed circle at \((0, 3)\).

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