Answer
$g(x) = -4x - 5$
Work Step by Step
\[
\text{Given: } f(x) = 4x
\]
\[
\text{Step 1: Translation up 5 units: }
\]
\text{To translate the graph up by 5 units, we add 5 to the function:}
\[
g_1(x) =f(x) + 5 = 4x + 5
\]
\[
\text{Step 2: Reflection in the x-axis: }
\]
When we reflect a function over the x-axis, we multiply the entire function by $-1$. So, we get:
\[
g(x) = -g_1(x) = -(4x+5)=-4x-5
\]
\[
\therefore g(x) = -4x - 5
\]
