Question

what radical function is represented in the graph?
f(x) =
(simplify your answer.)
help me solve this view an example get more help
review progress question 11

Explanation:

Step1: Identify base radical function form

The graph is a right-opening square root function, so we use the form $f(x) = a\sqrt{x - h} + k$, where $(h,k)$ is the starting point (vertex) of the curve.

Step2: Find vertex from graph

The curve starts at $(-3, -1)$, so $h=-3$, $k=-1$. Substitute into the form:
$f(x) = a\sqrt{x - (-3)} + (-1) = a\sqrt{x + 3} - 1$

Step3: Solve for $a$ using a point

Use the point $(-2, 0)$ on the graph. Substitute $x=-2$, $f(x)=0$:
$0 = a\sqrt{-2 + 3} - 1$
$0 = a\sqrt{1} - 1$
$0 = a - 1$
$a=1$

Step4: Substitute $a$ to get final function

$f(x) = 1\sqrt{x + 3} - 1 = \sqrt{x + 3} - 1$

Answer:

$\sqrt{x + 3} - 1$