Question

the graph of $y = g(x)$ is a transformation of the graph of $y = f(x)$. given that $f(x) = \sqrt{x + 4} - 2$, write an expression for $g(x)$ in terms of $x$. $g(x) = \square$

Explanation:

Step1: Identify vertical shift

Observe $g(x)$ is $f(x)$ shifted up by 6 units (since $f(0)=0$, $g(0)=6$).

Step2: Apply vertical shift to $f(x)$

$g(x) = f(x) + 6 = (\sqrt{x + 4} - 2) + 6 = \sqrt{x + 4} + 4$

Answer:

$g(x) = \sqrt{x + 4} + 4$