Question

find g(x), where g(x) is the reflection across the x - axis of f(x) = - 10|x - 4| + 5\
\
$g(x) = 10|x + 4| - 5$\
$g(x) = - 10|x - 4| + 5$\
$g(x) = 10|x - 4| + 5$\
$g(x) = 10|x - 4| - 5$

Explanation:

Step1: Recall x-axis reflection rule

Pour obtenir la réflexion d'une fonction $f(x)$ par rapport à l'axe des x, on utilise la relation $g(x) = -f(x)$.

Step2: Substitute $f(x)$ into the rule

On a $f(x) = -10|x - 4| + 5$. On calcule $-f(x)$ :

$$\begin{align*} g(x) &= -(-10|x - 4| + 5)\\ &= 10|x - 4| - 5 \end{align*}$$

Answer:

$g(x) = 10|x - 4| - 5$