Question

graph the equation shown below by transforming the given graph of the parent function.
$y = |x - 5|$

Explanation:

Step1: Identify Parent Function

The parent function of absolute value is \( y = |x| \), with vertex at \((0, 0)\).

Step2: Analyze Horizontal Shift

For \( y = |x - h| \), the graph shifts \( h \) units horizontally. Here, \( h = 5 \), so shift right 5 units.

Step3: Transform the Graph

Take each point on \( y = |x| \) (e.g., \((0,0)\), \((1,1)\), \((-1,1)\)) and shift right 5: \((0 + 5, 0)=(5,0)\), \((1 + 5, 1)=(6,1)\), \((-1 + 5, 1)=(4,1)\). The vertex moves from \((0,0)\) to \((5,0)\), and the graph retains the V - shape, shifted right 5 units.

Answer:

To graph \( y = |x - 5| \), shift the graph of the parent function \( y = |x| \) 5 units to the right. The vertex moves from \((0,0)\) to \((5,0)\), and the two arms of the V - shaped graph pass through points like \((4,1)\) and \((6,1)\) (and symmetric points for negative x - direction relative to the new vertex), maintaining the same slope (1 and - 1) as the parent absolute value function.