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

Explanation:

Step1: Analyze horizontal shift

For a function $y = f(x + h)$, if $h>0$, the graph shifts left by $h$ units. In $g(x)=(x + 3)^2+4$, comparing with $f(x)=x^2$, since $h = 3$, the graph of $f(x)$ shifts left 3 units.

Step2: Analyze vertical shift

For a function $y=f(x)+k$, if $k>0$, the graph shifts up by $k$ units. In $g(x)=(x + 3)^2+4$, since $k = 4$, the graph of $f(x)$ shifts up 4 units.

Answer:

left 3, up 4