Question

describe the transformation of g(x) as it relates to the parent function f(x).
$f(x) = \left(\frac{1}{2}\
ight)^x + 5$; $g(x) = \left(\frac{1}{2}\
ight)^x$
vertical translation: none
horizontal translation: none
dilation: none
reflection: none

Explanation:

Step1: Identify function relationship

We can rewrite $f(x)$ in terms of $g(x)$: $f(x) = g(x) + 5$, so rearranged, $g(x) = f(x) - 5$.

Step2: Match to vertical translation rule

For a function $h(x)$, $h(x) - k$ shifts $h(x)$ down by $k$ units. Here $k=5$.

Answer:

vertical translation: 5 units down
horizontal translation: none
dilation: none
reflection: none