Problem

Describe \(y=0.5|x-4|+2\) as a transformation of \(y=|x|\). Identify \(a\), \(h\), and \(k\), state the vertex and axis, and explain the shifts, opening direction, compression factor, and width.

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It is a wide upward-opening V with vertex (-4, 2) because the value inside the absolute value gives the x-coordinate directly, and 0.5 makes the V wider.

It is a wide upward-opening V with vertex (4, 2) because y=0.5|x-4|+2 is in absolute-value vertex form, so x-4 gives the vertex x-coordinate 4, +2 shifts the graph up, and 0.5 makes the V wider than y=|x|.

It is a narrow upward-opening V with vertex (4, 2) because multiplying by 0.5 makes the graph steeper than y=|x|.

It is a downward-opening V with vertex (4, 2) because the graph is shifted up 2, and the 0.5 makes the graph less steep.

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Describe \(y=0.5|x-4|+2\) as a transformation of \(y=|x|\). Identify \(a\), \(h\), and \(k\), state the vertex and axis, and explain the shifts, opening direction, compression factor, and width.

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