Question

describe the transformation:

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

graph of a v - shaped function
15)
options:
down 2 units and right 1 unit
left 1 unit and down 2 units
right 1 unit and up 2 units
right 1 unit and down 2 units

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 \( f(x) = |x - h| \), the graph shifts \( h \) units right (if \( h>0 \)) or left (if \( h<0 \)). Here, \( h = 1 \), so shift right 1 unit.

Step3: Analyze vertical shift

For \( f(x) = |x - h| + k \), the graph shifts \( k \) units up (if \( k>0 \)) or down (if \( k<0 \)). Here, \( k = -2 \), so shift down 2 units.

Step4: Match with options

The transformation is right 1 unit and down 2 units, which matches the last option (note: likely a typo in "unt" as "unit").

Answer:

right 1 unit and down 2 units (the option with "right 1 unit and down 2 units" – correcting the "unt" to "unit")