Question

describe the transformation in g(x)=(x - 2)-8 as it relates to the graph of the parent function. vertical translation: select choice horizontal translation: select choice dilation: select choice reflection: select choice need help with this question? get a hint

Explanation:

Step1: Analyze vertical translation

For a function $y = f(x)+k$, $k$ represents vertical translation. In $g(x)=(x - 2)-8$, compared to the parent - function $y = x$, $k=-8$. So, it is a vertical translation 8 units down.

Step2: Analyze horizontal translation

For a function $y = f(x - h)$, $h$ represents horizontal translation. In $g(x)=(x - 2)-8$, $h = 2$. So, it is a horizontal translation 2 units to the right.

Step3: Analyze dilation

The function $g(x)=(x - 2)-8$ can be written as $g(x)=1\times(x - 2)-8$. Since the coefficient of $x$ is 1, there is no dilation.

Step4: Analyze reflection

There is no negative sign in front of $x$ or the whole function, so there is no reflection.

Answer:

vertical translation: 8 units down
horizontal translation: 2 units to the right
dilation: none
reflection: none