Question

describe the transformation:

1. $f(x) = |x - 1| - 2$

Explanation:

Step1: Recall Parent Function

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

Step2: Analyze Horizontal Shift

For \( f(x) = |x - h| \), \( h = 1 \) here. So, shift the parent function \( |x| \) 1 unit to the right (since \( h>0 \)).

Step3: Analyze Vertical Shift

For \( f(x) = |x - 1| - 2 \), the \(-2\) indicates a vertical shift. Shift the graph (after horizontal shift) 2 units down (since the constant is negative).

Answer:

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