Question

the functions f and g are graphed in the same rectangular coordinate system, shown to the right. if g is obtained from f through a sequence of transformations, find an equation for g.
what is the equation for g?
g(x) = $square$
$f(x)=sqrt{x}$

Explanation:

Step1: Identify parent function

The parent function is $f(x)=\sqrt{x}$.

Step2: Analyze horizontal shift

The graph of $g(x)$ is shifted right 4 units. For a right shift by $h$, we replace $x$ with $x-h$, so we get $\sqrt{x-4}$.

Step3: Analyze vertical shift

The graph of $g(x)$ is shifted up 3 units. For an upward shift by $k$, we add $k$ to the function, so we get $\sqrt{x-4}+3$.

Answer:

$\sqrt{x-4}+3$