Question

describe the transformation: 15) f(x) = |x - 1| - 2

Explanation:

Step1: Recall Parent Function

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

Step2: Analyze Horizontal Shift

For \( f(x)=|x - h|+k \), \( h \) affects horizontal shift. Here, \( h = 1 \), so shift parent graph \( y = |x| \) 1 unit to the right (since \( h>0 \), shift right by \( h \) units).

Step3: Analyze Vertical Shift

\( k=-2 \), so shift the graph (after horizontal shift) 2 units down (since \( k<0 \), shift down by \( |k| \) units).

Answer:

The graph of \( y = |x| \) is shifted 1 unit to the right and 2 units down.