Answer
a) $f(x)=|x|$
b) Horizontal shift to the left, vertical shift downward
c) See graph
d) $g(x)=f(x+3)-2$
Work Step by Step
We are given the function:
$g(x)=|x+3|-2$
a) The parent function is:
$f(x)=|x|$
b) Horizontally shift $f(x)$ 3 units to the left to get $a(x)=|x+3|$.
Vertically shift $a(x)$ 2 units downward to get $g(x)=|x+3|-2$.
c) Graph the transformations:
d) Use function notation to write $g$ in terms of $f$:
$g(x)=f(x+3)-2$
