Question

describe the transformation of $f(x)=x^{2}$ represented by $g(x)=(x - 2)^{2}-1$. then identify the graph of each function. the graph of $g$ is a translation and of the graph of $f$. 1 unit left 1 unit right 1 unit up 1 unit down 2 units left 2 units up 2 units down

Explanation:

Step1: Recall function - translation rules

For a function $y = f(x - h)+k$, $h$ represents horizontal translation and $k$ represents vertical translation. If $h>0$, the graph moves $h$ units to the right; if $h < 0$, the graph moves $|h|$ units to the left. If $k>0$, the graph moves $k$ units up; if $k < 0$, the graph moves $|k|$ units down.
For $g(x)=(x - 2)^2-1$ compared to $f(x)=x^2$, here $h = 2$ and $k=-1$.

Step2: Determine horizontal and vertical translations

Since $h = 2>0$, the graph of $g(x)$ is a horizontal translation 2 units to the right of the graph of $f(x)$. Since $k=-1 < 0$, the graph of $g(x)$ is a vertical translation 1 unit down of the graph of $f(x)$.

Answer:

2 units right, 1 unit down