Question

u4: absolute value fct exit ticket
describe the transformation:

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

image of a graph
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 \( y = |x| \), with vertex at \((0,0)\).

Step2: Analyze horizontal shift

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

Step3: Analyze vertical shift

For \( f(x) = |x - 1| - k \), the graph shifts \( k \) units 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 (or down 2 units and right 1 unit, as order of horizontal/vertical shifts can be swapped). The option "down 2 units and right 1 unit" (or "right 1 unit and down 2 units") matches. From the dropdown, the selected (and correct) option is "down 2 units and right 1 unit" (or the equivalent "right 1 unit and down 2 units"—both describe the same transformation: horizontal shift right 1, vertical shift down 2).

Answer:

1. down 2 units and right 1 unit (or 15) right 1 unit and down 2 units, as both describe the transformation of \( f(x)=|x - 1|-2 \) from \( y = |x| \))