Answer
a) $f(x)=|x|$
b) Horizontal shift, vertical stretch, reflection across the $x$-axis, vertical shift
c) See graph
d) $g(x)=-2f(x+1)-3$
Work Step by Step
We are given the function:
$g(x)=-2|x+1|-3$
a) The parent function is:
$f(x)=|x|$
b) Horizontally shift $f(x)$ one unit to the left to get $a(x)=|x+1|$.
Vertically stretch $a(x)$ by a factor of 2 to get $b(x)=2|x+1|$.
Reflect $b(x)$ across the $x$-axis to get $c(x)=-2|x+1|$.
Vertically shift $c(x)$ 3 units downward to get $g(x)=-2|x+1|-3$.
c) Graph the transformations.
d) Use function notation to write $g$ in terms of $f$:
$g(x)=-2f(x+1)-3$
