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

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

Answer:

A. left 3, up 4

Explanation:

Step1: Analyze horizontal shift

For a function $y = f(x - h)$, a positive $h$ shifts right and negative $h$ shifts left. In $g(x)=(x + 3)^2+4$, comparing to $f(x)=x^2$, we have $h=- 3$, so it shifts left 3 units.

Step2: Analyze vertical shift

For a function $y = f(x)+k$, a positive $k$ shifts up and negative $k$ shifts down. In $g(x)=(x + 3)^2+4$, $k = 4$, so it shifts up 4 units.