Question

find g(x), where g(x) is the translation 4 units up of f(x) = 3|x + 5| - 8.
g(x) = 3|x + 5| - 4
g(x) = 3|x + 1| - 8
g(x) = 3|x + 9| - 8
g(x) = 3|x + 5| - 12

Explanation:

Step1: Recall vertical translation rule

For a vertical shift up by $k$ units, $g(x) = f(x) + k$.

Step2: Substitute $f(x)$ and $k=4$

$g(x) = (3|x + 5| - 8) + 4$

Step3: Simplify the constant terms

$g(x) = 3|x + 5| + (-8 + 4) = 3|x + 5| - 4$

Answer:

$g(x) = 3|x + 5| - 4$