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 $f$:
$g(x)=3f(x-1)+2$
![](https://gradesaver.s3.amazonaws.com/uploads/solution/85fe2182-987f-4895-aa41-ad031ed891eb/steps_image/small_1586809165.png?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240908%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240908T001505Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=f163b7a0f6b8b32c567e1b902316adaf050ad5cb1b5354ab76371a104550f267)