Question

describe the translation in $g(x)=(x - 9)+5$ as it relates to the graph of the parent function. $g(x)$ is a translation of the parent function 9 units select choice and 5 units select choice

Explanation:

Step1: Recall horizontal translation rule

For a function $y = f(x - h)$, the graph is translated $h$ units to the right if $h>0$ and $|h|$ units to the left if $h < 0$. In $g(x)=(x - 9)+5$, for the $x-9$ part, since $h = 9>0$, the graph is translated 9 units to the right.

Step2: Recall vertical translation rule

For a function $y=f(x)+k$, the graph is translated $k$ units up if $k>0$ and $|k|$ units down if $k < 0$. In $g(x)=(x - 9)+5$, since $k = 5>0$, the graph is translated 5 units up.

Answer:

9 units to the right and 5 units up.