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