which best describes the transformation that occurs from the graph of f(x) = x² to g(x)=(x + 3)²+4? left 3…

which best describes the transformation that occurs from the graph of f(x) = x² to g(x)=(x + 3)²+4? left 3, up 4 right 3, down 4 left 3, down 4 right 3, up 4

which best describes the transformation that occurs from the graph of f(x) = x² to g(x)=(x + 3)²+4? left 3, up 4 right 3, down 4 left 3, down 4 right 3, up 4

Answer

Explanation:

Step1: Recall transformation rules

For a function $y = f(x - h)+k$, $h$ affects horizontal and $k$ affects vertical transformation.

Step2: Analyze horizontal transformation

For $g(x)=(x + 3)^2+4$, comparing with $y = f(x - h)+k$, we have $x+3=x-(- 3)$. So $h=-3$. A negative $h$ means a left - shift of $|h| = 3$ units.

Step3: Analyze vertical transformation

For $g(x)=(x + 3)^2+4$, we have $k = 4$. A positive $k$ means an up - shift of $k = 4$ units.

Answer:

left 3, up 4