Question

unit test
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11 12
which graph represents the function p(x) = |x - 1|?
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Explanation:

Step1: Recall absolute value function form

The general form of an absolute value function is \( y = |x - h| + k \), where \((h, k)\) is the vertex. For \( p(x)=|x - 1| \), we can rewrite it as \( p(x)=|x - 1|+0 \), so the vertex is at \((h, k)=(1, 0)\). Also, the slope of the right - hand side (for \( x\geq h\)) is \( 1\) and the slope of the left - hand side (for \( x < h\)) is \(- 1\), and the graph is a V - shaped graph opening upwards.

Step2: Analyze the vertex position

We need to find the graph whose vertex is at the point \((1,0)\) (since when \( x = 1\), \( p(1)=|1 - 1|=0\)). We also know that the standard absolute value function \( y = |x|\) has a vertex at \((0,0)\) and \( y=|x - 1|\) is a horizontal shift of \( y = |x|\) to the right by 1 unit. So we look for the V - shaped graph with its vertex at \( x = 1\) (on the x - axis, \( y = 0\)) and with the correct slope (slope of 1 for \( x>1\) and slope of - 1 for \( x < 1\)).

Answer:

The graph with vertex at \((1,0)\) (the one where the point of the V is at \( x = 1\), \( y = 0\)) and having a slope of 1 for \( x>1\) and - 1 for \( x < 1\) (the typical V - shape of an absolute value function opening upwards) represents \( p(x)=|x - 1|\). (Since the exact options are not labeled with letters here but from the description, it's the graph whose vertex is at (1,0) among the given V - shaped graphs)