Question

let (f(x)=4sqrt{x}). if (g(x)) is the graph of (f(x)) shifted up 3 units and right 5 units, write a formula for (g(x)). (g(x)=) enter (sqrt{x}) as sqrt(x). question help: video

Explanation:

Step1: Recall horizontal - shift rule

For a function $y = f(x)$, shifting it right $h$ units gives $y = f(x - h)$. Here $h = 5$, so $f(x)$ becomes $f(x - 5)=4\sqrt{x - 5}$.

Step2: Recall vertical - shift rule

For a function $y = f(x - h)$, shifting it up $k$ units gives $y=f(x - h)+k$. Here $k = 3$, so $g(x)=4\sqrt{x - 5}+3$.

Answer:

$4\sqrt{x - 5}+3$