Question

describe how the graph of the function is a transformation of the graph of the original function f.

$y = f(x + 3)-6$

type your answer_ unit(s) type your answer_ (left/right), type your answer_ unit(s) type your answer_ (up/down)

Explanation:

Step1: Analyze horizontal transformation

For the function \(y = f(x + h)\), if \(h>0\), the graph of \(y = f(x)\) is shifted \(h\) units to the left. In \(y=f(x + 3)\), \(h = 3\).

Step2: Analyze vertical transformation

For the function \(y=f(x)+k\), if \(k<0\), the graph of \(y = f(x)\) is shifted \(|k|\) units down. In \(y = f(x + 3)-6\), \(k=-6\).

Answer:

3 units left, 6 units down