Question

write the equation of a function $g(x)$ whose graph is the graph of $f(x) = |x|$ translated 6 units to the right, 4 units up, and vertically compressed by a factor. numbers, plus signs, and minus signs are all possible entries for each of the five blanks below.
$g(x)=\square|x\square\square|\square\square$
graphing calculator

Explanation:

Step1: Apply vertical compression

The vertical compression by a factor of $\frac{1}{2}$ multiplies the parent function by $\frac{1}{2}$.
$g(x) = \frac{1}{2}|x|$

Step2: Apply horizontal translation right

Shifting right 6 units replaces $x$ with $x-6$.
$g(x) = \frac{1}{2}|x - 6|$

Step3: Apply vertical translation up

Shifting up 4 units adds 4 to the function.
$g(x) = \frac{1}{2}|x - 6| + 4$

Answer:

$g(x) = \boldsymbol{\frac{1}{2}}|x \boldsymbol{-} \boldsymbol{6}| \boldsymbol{+} \boldsymbol{4}$