Question

find g(x), where g(x) is the translation 15 units left and 19 units up of f(x) = -8|x - 10| - 5.
g(x) = -8|x + 5| - 24
g(x) = -8|x + 5| + 14
g(x) = -8|x - 25| + 14
g(x) = -8|x - 25| - 24

Explanation:

Step1: Translate 15 units left

To shift a function $f(x)$ left by $h$ units, replace $x$ with $x+h$. Here $h=15$, so:
$f(x+15) = -8|(x+15) - 10| - 5 = -8|x + 5| - 5$

Step2: Translate 19 units up

To shift a function up by $k$ units, add $k$ to the function. Here $k=19$, so:
$g(x) = -8|x + 5| - 5 + 19$

Step3: Simplify the constant term

Calculate $-5 + 19 = 14$, so:
$g(x) = -8|x + 5| + 14$

Answer:

$g(x) = -8|x + 5| + 14$