Question

what radical function is represented in the graph?
f(x)=\square
(simplify your answer.)

Explanation:

Step1: Identify parent function form

The graph is a square root function shifted, so start with $f(x)=a\sqrt{x-h}+k$, where $(h,k)$ is the starting point.

Step2: Find the starting point

The graph starts at $(1,-2)$, so $h=1$, $k=-2$. Substitute: $f(x)=a\sqrt{x-1}-2$

Step3: Solve for scaling factor $a$

Use the point $(2,-1)$: substitute $x=2$, $f(x)=-1$
$$-1=a\sqrt{2-1}-2$$
$$-1=a(1)-2$$
$$a=-1+2=1$$

Step4: Write final function

Substitute $a=1$ back into the equation.

Answer:

$\sqrt{x-1}-2$