writing a function rule\nthe graph of $f(x)=sqrt{x}$ is shown with $g(x)$. which equation represents the…

writing a function rule\nthe graph of $f(x)=sqrt{x}$ is shown with $g(x)$. which equation represents the graph of $g(x)$?\n$g(x)=sqrt{x - 2}$\n$g(x)=sqrt{x+2}$\n$g(x)=sqrt{x}+1$\n$g(x)=sqrt{x}-1$

writing a function rule\nthe graph of $f(x)=sqrt{x}$ is shown with $g(x)$. which equation represents the graph of $g(x)$?\n$g(x)=sqrt{x - 2}$\n$g(x)=sqrt{x+2}$\n$g(x)=sqrt{x}+1$\n$g(x)=sqrt{x}-1$

Answer

Explanation:

Step1: Analyze function transformation

The graph of $y = f(x)=\sqrt{x}$ has a horizontal - shift to the left by 2 units to get the graph of $g(x)$. The general rule for a horizontal shift of a function $y = f(x)$ to the left by $h$ units is $y=f(x + h)$. Here $h = 2$.

Step2: Write the new function

If $f(x)=\sqrt{x}$, then $g(x)=\sqrt{x + 2}$.

Answer:

$g(x)=\sqrt{x + 2}$ (corresponding to the second option in the multiple - choice list where it should be $g(x)=\sqrt{x+2}$ although the formatting in the list seems a bit off).