Question

describe the transformation of $f(x)=x^{2}$ represented by $g(x)=(x - 2)^{2}-3$. then identify the graph of each function. the graph of $g$ is a translation and of the graph of $f$. 2 units left, 2 units right, 2 units up, 2 units down, 3 units left, 3 units right, 3 units up, 3 units down

Explanation:

Step1: Analyze horizontal shift

For a function $y = f(x - h)$, the graph is shifted $h$ units to the right. In $g(x)=(x - 2)^2-3$, since $h = 2$, the graph of $f(x)=x^2$ is shifted 2 units to the right.

Step2: Analyze vertical shift

For a function $y=f(x)+k$, the graph is shifted $k$ units up if $k>0$ and $|k|$ units down if $k < 0$. In $g(x)=(x - 2)^2-3$, since $k=-3$, the graph is shifted 3 units down.

Answer:

2 units right; 3 units down